In chronological order:
St. Cyprian, 3rd century: “Where Peter is, there is the Church”, repeated by St. Ambrose and St. Boniface. Confirmed by Pope Benedict XV in the Encyclical In Hac Tanta.
St. Cyprian: “If someone does not hold fast to this unity of Peter, can he imagine that he still holds the faith? If he should desert the chair of Peter upon whom the Church was built, can he still be confident that he is in the Church?”
Pope Saint Lucius I, Martyr, 253-254: “The Roman Apostolic Church is the mother of all Churches and has never been shown to have wandered from the path of Apostolic tradition, nor being deformed, succumbed to heretical novelties according to the promise of the Lord himself, saying, ‘I have prayed for thee, etc.’ [Lk 22:32]” [Epist. I ad Episcopos Hispaniae et Galliae]
Pope Saint Felix I, 269-274, speaking on the Roman Church: “As it took up in the beginning the norm of the Christian Faith from its authors, the Princes of the Apostles of Christ [i.e. the Popes], She remains unsullied according to what the Lord said: ‘I have prayed for thee, etc.’ [Lk 22:32]” [Bellarmine, Robert. On the Roman Pontiff, vol. 2: Books III-V (De Controversiis) (p. 157-158). Mediatrix Press. Kindle Edition.]
Saint Jerome, 4th century: “The welfare of the Church depends on the dignity of the papacy. If we do not give the pope sovereign and independent power, there will be as many schisms in the Church as there are priests.” Confirmed by Pope Benedict XV in the Encyclical In Hac Tanta.
Pope Saint Zosimus (417-418): “the tradition of the Fathers attributed so much authority to the Apostolic See that no one dared to challenge its judgment and has always preserved it through canons and regulations … such great authority belongs to Us that no one could argue again with Our decision….”
Pope Saint Boniface I (418-22), Letter to the Bishop of Thessalonica: “there is to be no review of our judgment. In fact, it has never been licit to deliberate again on that which has once been decided by the Apostolic See.”
Pope Saint Boniface I, Letter to the Bishops of Macedonia: “No one has ever boldly raised his hands against the apostolic eminence, from whose judgment it is not permissible to dissent; no one has rebelled against this who did not wish judgment to be passed upon him.”
Saint Peter Chrysologus, 406-450: “We exhort you, Honorable Brother, that you would obediently attend to that which has been written by the Pope of the city of Rome because Blessed Peter, who lives in his own See and presides there, is in charge of all those seeking the truth of faith.” [Ibid.]
Saint Bernard: “It is fitting that every danger and scandal of the kingdom of God be referred to your Apostolate and especially these which touch upon the faith. For I regard it worthy that there, above all, dangers to the faith are mended, where one cannot think the faith is lacking. For to what other See was it ever said: ‘I have prayed for thee, that thy faith not fail?’ [Lk 22:32] ” [Epist. 190 ad Innocentium]
Origen says: “It is manifest, even if it were not expressed, because the gates of Hell can prevail against neither Peter nor the Church, for if they prevailed against the rock on which the Church was founded, they would prevail against the Church.” [Mt 16:18] [Bellarmine, Robert. On the Roman Pontiff, vol. 2: Books III-V (De Controversiis) (p. 160). Mediatrix Press. Kindle Edition.]
Saint Cyril says: “According to this promise of the Lord, the Apostolic Church of Peter remains pure and spotless from all leading into error, or heretical fraud, above all Heads and Bishops, and Primates of Churches and people, with its own Pontiffs, with most abundant faith, and the authority of Peter. And while other Churches have to blush for the error of some of their members, this [See of Peter] reigns alone, immovably established, enforcing silence, and stopping the mouths of all heretics; [et nos necessario salutis] and we, from necessity of salvation, not drunken with the wine of pride, confess, together with it, the formula of truth and of the holy apostolic tradition.” [Catena Aurea of St. Thomas on Mt 16:18; edited by the author]
“Every true Catholic proclaims with St. Cyprian and St. Augustine: ‘He cannot have God as his Father who does not have the Church as his Mother.’ ”
Pope Saint Leo the great (Leo I) 440-461: “The special care of Peter is received from the Lord; he prayed for the faith of Peter in particular in as much as the state of the others would be more certain if the mind of the Prince were not conquered. Therefore, in Peter the strength of all is fortified and the help of divine grace is so ordered that the strength which was given to Peter through Christ would be conferred through Peter to the remaining Apostles.” [Ibid.]
Theodoret said: “This holy See holds the reign of the Churches of the world, not only on account of other things, but also because she remains free from the heretical stench.” [Epistola ad Renatum Presbyterum Romanum]
Pope Saint Gelasius I, 492-96, epistle to the Emperor Anastasius: “This is what the Apostolic See guards against with all her strength because the glorious confession of the Apostle is the root of the world, so that she is polluted by no crack of depravity and altogether no contagion. For if such a thing would ever occur (which may God forbid and we trust cannot be), why would we make bold to resist any error?” [Bellarmine, Robert. On the Roman Pontiff, vol. 2: Books III-V (De Controversiis) (p. 161). Mediatrix Press. Kindle Edition.]
Saint Gregory the Great, 590-604: “Who does not know that the whole Church was strengthened in the firmness of the Prince of the Apostles, to whom it was said, ‘Upon this rock I will build my Church … and thou, being converted, confirm thy brethren?’ [Lk 22:32] ” [Lib. 7, epist. 37 ad Eulogium] Saint Bellarmine: “There Gregory clearly teaches the strength of the Church depends upon the strength of Peter, and hence Peter is less able to err than the Church herself.” [Ibid.]
The example of Pope Vigilius, d. 555, as related by Saint Robert Bellarmine: “For he received with the pontificate the strength of faith and he was changed from a weak chaff into the most solid rock.”
Pope Pelagius II, 590 AD: To the Bishops of Istria, writes: “For you know how the Lord in the Gospel declares: ‘Simon, Simon, behold Satan has desired you that he might sift you as wheat, but I have prayed the Father for thee, that thy faith fail not, and thou being converted, confirm thy brethren.’ See, beloved, the truth cannot be falsified, nor can the faith of Peter ever be shaken or changed.”
Sergius of Cyprus, his letter approved by Pope Saint Martin, 643: “Christ our God founded your apostolic see, O sacred head, as a divinely fixed and immovable support and conspicuous inscription of the faith. For you, as the divine Word truly declared without deceit, are Peter, and on your foundation the pillars of the church are fixed; to you he committed the keys of the heavens and decreed that you are to bind and loose with authority on earth and in heaven. You have been made the destroyer of profane heresies, as the leader and teacher of the orthodox and unimpeachable faith.” [Price, Acts of Lateran, p. 157-160]
Stephen of Dora – “And again, because he [Peter] possessed more than all others, in an exceptional and unique way, firm and unshakeable faith in our Lord, [he was deemed worthy] to turn and strengthen his comrades and spiritual brethren when they were wavering, since providentially he had been adorned by the God who became incarnate for our sake with power and priestly authority over them all.” [See his Letter accepted by the (local) Lateran Council of 649]
Pope Saint Agatho, 680 AD: “For Peter himself received from the Redeemer of all, by three commendations, the duty of feeding the spiritual sheep of the Church. Under his protecting shield, this Apostolic Church of his has never turned away from the path of truth in any direction of error.”
“And his authority, as that of the Prince of all the Apostles, the whole Catholic Church and the Ecumenical Synods have faithfully embraced and followed in all things.”
“but from the beginning she has received the Christian faith from her founders, the princes of the Apostles of Christ, and remains undefiled unto the end….”
“…the evangelical and apostolic uprightness of the orthodox faith, which has been established upon the firm rock of this Church of blessed Peter, the Prince of the Apostles, which by his grace and guardianship remains free from all error….” [Letter to the Sixth Ecumenical Council 680 AD]
Saint Theophylactus, Saint Bellarmine explains, “openly teaches that this privilege was given to Peter because he was going to be the prince and head of others; hence it was given to all the others that would succeed him in that supremacy: ‘Because I have you as a prince of the disciples, confirm the others. This is fitting for you, who are the rock of the Church after me, as well as the foundation.’ ” [Bellarmine, Robert. On the Roman Pontiff, vol. 2: Books III-V (De Controversiis) (p. 159). Mediatrix Press. Kindle Edition.]
Pope Saint Nicholas I, 860 AD: “If anyone condemns dogmas, mandates, interdicts, sanctions, or decrees, promulgated by the one presiding in the Apostolic See, for the Catholic faith, for the correction of the faithful, for the emendation of criminals, either by an interdict of threatening or of future ills, let him be anathema.” [Roman Council 860 and 863; Denzinger 326]
Pope Saint Nicholas I “Neither by the emperor nor by all the clergy nor by kings nor by the people will the judge be judged…. The first See will not be judged by anyone.” [Denzinger n. 638]
Pope Saint Nicholas I “Certainly it is evident that the judgment of the Apostolic See, of whose authority there is none greater, is to be refused by no one … the judgment of the Roman bishop being no longer open for reconsideration. [Letter Proposueramus quidem to Emperor Michael, September 28, 865; Denz. 641]
Pope Saint Nicholas I “The privileges of this see are perpetual, divinely rooted and also planted. One can strike against them but not transfer them; one can drag them but not tear them out. Those matters which were formerly your imperium remain, thanks be to God, insofar as they are inviolate; they will remain after you and so long as the Christian name will be preached, they will not cease to exist. . . . For among other things, these privileges are especially conferred through us, ‘Thou later being converted,’ he heard from the Lord, ‘confirm thy brethren.’ [Lk 22:32] ” [Epistlola ad Michaelem Imperatorem]
Pope Saint Leo IX (1049-54) in an Epistle to Peter of Antioch: “Without a doubt, it was for he alone whom the Lord and Savior asserted that he prayed that his faith would not fail, saying, ‘I have prayed for thee, etc.’ [Lk 22:32]. Such a venerable and efficacious prayer obtained that to this point the faith of Peter has not failed, nor can it be believed that it is ever going to fail in his throne.” [Bellarmine, Robert. On the Roman Pontiff, vol. 2: Books III-V (De Controversiis) (p. 158). Mediatrix Press. Kindle Edition.]
Pope Saint Leo IX, 1053 AD: “By the See of the Chief of the Apostles, namely by the Roman Church, through the same Peter, as well as through his successors, have not the comments of all the heretics been disapproved, rejected, and overcome, and the hearts of the brethren in the faith of Peter — which so far neither has failed, nor up to the end will fail — been strengthened?” [In Terra Pax Hominibus, September 2, 1053; Denz. 351]
Pope Saint Leo IX, 1053: “By passing a preceding judgment on the great See, concerning which it is not permitted any man to pass judgment, you have received anathema from all the Fathers of all the venerable Councils….”
“As the hinge while remaining immovable opens and closes the door, so Peter and his successors have free judgment over all the Church, since no one should remove their status because ‘the highest See is judged by no one.’ ” [Epistle: In Terra Pax Hominibus; Denzinger 351-353.]
Pope Innocent III (1198-1216), Epistle to the Bishop of Arles: “The Fathers, for the sake of the Church, understood especially in regard to articles of faith that those words refer to the See of Peter, who knew the Lord had prayed for him, lest his faith would fail.” [Ibid.]
St. Thomas Aquinas (1225-1274) wrote much on this topic. See the extensive treatment of his support for the unshakeable faith of the Pope here. “He argued that although the heresies existed in other church — Constantinople was the typical example – through the centuries the Church of Rome alone had kept its faith whole. In it, Christ’s prayer (i.e. to Peter of unfailing faith [Lk 22:32]) is fulfilled, and from it the true faith had spread to the entire Western Church. Yet here there is an important additional claim: that the faith remained whole was due not only to the Roman church, but also to the faith of St. Peter” (The Dominicans and the Pope: Papal Teaching Authority in the Medieval and Early Modern Thomist Tradition, Ulrich Horst, O.P. , page 18).
Pope Boniface VIII, 1302 AD, Unam Sanctam, a document later confirmed by the Fifth Lateran Council:
3. “And so, the one and only Church is one body, one head, (not two heads like a monster), Christ certainly, and the vicar of Christ, [who is ] Peter and the successor of Peter.” [The teaching on one head was later confirmed by Pope Pius XII in Mystici Corporis Christi.]
“7. Therefore, if the earthly power goes astray, it will be judged by the spiritual power; but if a lesser spiritual power goes astray, [it will be judged] by its superior; and truly, if the highest [power] goes astray, it will not be able to be judged by man, but by God alone. And so the Apostle testifies, ‘The spiritual man judges all things, but he himself is judged by no one.’ [1 Corinthians 2:15]”
“8. But this authority, even though it may be given to a man, and may be exercised by a man, is not human, but rather divine [power], having been given by the divine mouth [of Christ] to Peter, and to him as well as to his successors, by [Christ] Himself, [that is, to him] whom He had disclosed to be the firm rock, just as the Lord said to Peter himself: ‘Whatever you shall bind,’ [Matthew 16:19] etc. Therefore, whoever resists this authority, such as it has been ordain by God, resists the ordination of God. [Romans 13:2]”
“9. Moreover, that every human creature is to be subject to the Roman pontiff, we declare, we state, we define, and we pronounce to be entirely from the necessity of salvation.” [Unam Sanctam, 1302; Fifth Lateran Council, 1512-1517]
Pope Clement VI (1342-52) — “whether you have believed and do believe that the supreme and preeminent authority and juridical power of those who were the Roman pontiffs, We who are so, and those who will be so in the future have been, are, and will be such that they and We were not, are not, and in the future will not be able to be judged by anyone; but that they and We have been, are, and will be reserved in judgment by God alone; and that it was not possible, is not possible, and will not be possible for Our decisions and judgments to be appealed to any other judge.” [Letter “Super quibusdam” to the Consolator, Catholiciso of the Armenians, September 29, 1351; p. 310, Denz. 1056]
Pope Gregory XI (1370-78) — Condemned the Error: “An ecclesiastic, even the roman pontiff, can legitimately be corrected, and even accused, by subjects and lay persons.” [Error n. 19, Errors of John Wycliffe, Condemned in the Letter “Super periculosis” to the Bishops of Canterbury and London, May 22, 1377; Denz. 1139]
St. Robert Bellarmine (1542-1621) interpreting the words of our Lord in Lk. 22:32, states that “the true exposition” is that Jesus prayed for a privilege for Peter and his successors that “without doubt” (sine dubio) the privilege has been handed down to Peter’s successors, which insures that “in his chair there would never be found someone who would teach contrary to the true faith” (in sede ejus numquam inveniretur qui doceret contra veram Fidem). [On the Supreme Pontiff, book iv, chapter 3]
Bellarmine: “A general Council represents the universal Church, and hence has the consensus of the universal Church; wherefore if the Church cannot err, neither can a legitimate and approved ecumenical Council err.” (Concilium generale repraesentat Ecclesiam universam, et proinde consensus habet Ecclesiam universalis; quare si Ecclesia non potest errare, neque Concilium oecumenicum legitimum, et approbatum potest errare). [On Councils, book II, chapter 2]
Bellarmine: interpreting Luke 22:31-32, states: “Therefore, the true exposition is that the Lord asked for two privileges for Peter.” The first was Peter’s perseverance in grace (love, faith, hope) to the end, which was not handed down to his successors. [Thus, some Popes can sin gravely.] “The second privilege is that he, as the Pope, could never teach something against the faith, or that there would never be found one in his See who would teach against the true faith.” (in sede ejus numquam inveniretur qui doceret contra veram Fidem). “From these privileges, we see that the first did not remain to his successors, but the second without a doubt did.” [On the Supreme Pontiff, book IV, chapter 3]
Saint Bellarmine: “The Pope is the Teacher and Shepherd of the whole Church, thus, the whole Church is so bound to hear and follow him that if he would err, the whole Church would err.” [Bellarmine, Robert. On the Roman Pontiff, vol. 2: Books III-V (De Controversiis) (p. 162). Mediatrix Press. Kindle Edition.]
Saint Bellarmine: “Now our adversaries respond that the Church ought to hear him [the Roman Pontiff] so long as he teaches correctly, for God must be heard more than men. On the other hand, who will judge whether the Pope has taught rightly or not? For it is not for the sheep to judge whether the shepherd wanders off, not even and especially in those matters which are truly doubtful. Nor do Christian sheep have any greater judge or teacher to whom they might have recourse. As we showed above, from the whole Church one can appeal to the Pope; yet from him no one is able to appeal; therefore necessarily the whole Church will err, if the Pontiff would err.” [Bellarmine, Robert. On the Roman Pontiff, vol. 2: Books III-V (De Controversiis) (p. 162). Mediatrix Press. Kindle Edition.]
Note: Since the Church is indefectible, and can never go astray, the Roman Pontiff also can never go astray. Here Bellarmine does not assert that Popes are always free from every error, but only that they are free from errors that would lead one astray from the true Faith.
In 1651, eighty-five bishops of France wrote to Innocent X., praying that the five propositions of Jansenius might be judged by the Apostolic See. They say: ‘It is the solemn custom of the Church to refer the greater causes to the Holy See, which custom the never-failing faith of Peter demands in his right that we should perpetually observe.’ ” [Cardinal Manning, Petri Privilegium, p. 102.]
Vatican I, 1870: “Since the Roman Pontiff, by the divine right of the apostolic primacy, governs the whole Church, we likewise teach and declare that he is the supreme judge of the faithful, and that in all cases which fall under ecclesiastical jurisdiction recourse may be had to his judgment. The sentence of the Apostolic See (than which there is no higher authority) is not subject to revision by anyone, nor may anyone lawfully pass judgment thereupon. And so they stray from the genuine path of truth who maintain that it is lawful to appeal from the judgments of the Roman pontiffs to an Ecumenical Council as if this were an authority superior to the Roman Pontiff.” [First Vatican Council, First dogmatic constitution on the church of Christ, Chapter 3, n. 8]
Vatican I, 1870: “6. For the Holy Spirit was promised to the successors of Peter, not so that they might, by His revelation, make known some new doctrine, but that, by His assistance, they might religiously guard and faithfully expound the Revelation or Deposit of Faith transmitted by the Apostles.
“Indeed, their Apostolic teaching was embraced by all the venerable fathers, and reverenced and followed by all the holy orthodox doctors, for they knew very well that this See of St. Peter always remains unblemished by any error, in accordance with the divine promise of our Lord and Savior to the prince of his disciples: ‘I have prayed for you that your faith may not fail; and when you have turned again, strengthen your brethren’ [Lk 22:32].
“This gift of truth and never-failing faith was therefore divinely conferred on Peter and his successors in this See so that they might discharge their exalted office for the salvation of all, and so that the whole flock of Christ might be kept away by them from the poisonous food of error and be nourished with the sustenance of heavenly doctrine.” [First Vatican Council, First dogmatic constitution on the church of Christ, Chapter 4, n. 7]
Cardinal Manning, 1870: “The application of the promise ‘Ego rogavi pro te,’ [“I have prayed for you”] etc. to the infallible faith of Peter and his successors, is made by St. Ambrose, St. Augustine, St. Leo, St. Gelasius, Pelagius II., St. Gregory the Great, Stephen Bishop of Dori in a Lateran Council, St. Vitalian, the Bishops of the IV Ecumenical Council AD 451, St. Agatho in the VI. AD 680, St. Bernard AD 1153, St. Thomas Aquinas AD 1274, St. Bonaventure AD 1274: that is, this interpretation is given by three out of the four Doctors of the Church, by six Pontiffs down to the seventh century. It was recognized in two Ecumenical Councils. It is expressly declared by the Angelic Doctor, who may be taken as the exponent of the Dominican school, and by the Seraphic Doctor, who is likewise the witness of the Franciscan; and by a multitude of Saints.”
“The interpretation by the Fathers of the words ‘On this rock,’ etc. is fourfold, but all four interpretations are not more than four aspects of one and the same truth, and all are necessary to complete its full meaning. They all implicitly or explicitly contain the perpetual stability of Peter’s faith….”
“In these two promises [i.e. Lk 22:32, Mt 16:18] a divine assistance is pledged to Peter and to his successors, and that divine assistance is promised to secure the stability and indefectibility of the Faith in the supreme Doctor and Head of the Church, for the general good of the Church itself.”
[Cardinal Manning, “The Vatican Council and Its Definitions: A Pastoral Letter to the Clergy”, p. 83-84.]
Bishop Vincent Gasser: “This prerogative granted to St. Peter by the Lord Jesus Christ was supposed to pass to all Peter’s successors because the chair of Peter is the center of unity in the Church. But if the Pontiff should fall into an error of faith, the Church would dissolve, deprived of the bond of unity. The Bishop of Meaux [French Bishop Auguste Allou] speaks very well on this point, saying: ‘If this Roman See could fall and be no longer the See of truth but of error and pestilence, then the Catholic Church herself would not have the bond of a society and would be schismatic and scattered — which in fact is impossible.’ ” [Relatio to the fathers of Vatican I by the deputation from Pope Pius IX]
Pope Leo XIII, 1890: “And since all Christians must be closely united in the communion of one immutable faith, Christ the Lord, in virtue of His prayers, obtained for Peter that in the fulfilment of his office he should never fall away from the faith. “But I have asked for thee that thy faith fail not” (Luke xxii., 32), and He furthermore commanded him to impart light and strength to his brethren as often as the need should arise: “Confirm thy brethren” (Ibid.). He willed then that he whom He had designated as the foundation of the Church should be the defence of its faith. “Could not Christ who confided to him the Kingdom by His own authority have strengthened the faith of one whom He designated a rock to show the foundation of the Church?” (S. Ambrosius, De Fide, lib. iv., n. 56).” [Satis Cognitum 12]
“Bishops are deprived of the right and power of ruling, if they deliberately secede from Peter and his successors; because, by this secession, they are separated from the foundation on which the whole edifice must rest. They are therefore outside the edifice itself; and for this very reason they are separated from the fold, whose leader is the Chief Pastor; they are exiled from the Kingdom, the keys of which were given by Christ to Peter alone.” [Satis Cognitum 15]
Pope Blessed Pius IX, 1873, on those who reject the teachings of the First Vatican Council: “For these writings attack and pervert the true power of jurisdiction of the Roman Pontiff and the bishops, who are the successors of blessed Peter and the apostles; they transfer it instead to the people, or, as they say, to the community. They obstinately reject and oppose the infallible magisterium both of the Roman Pontiff and of the whole Church in teaching matters. Incredibly, they boldly affirm that the Roman Pontiff and all the bishops, the priests and the people conjoined with him in the unity of faith and communion fell into heresy when they approved and professed the definitions of the Ecumenical Vatican Council. Therefore they deny also the indefectibility of the Church and blasphemously declare that it has perished throughout the world and that its visible Head and the bishops have erred.” (Etsi Multa 22).
Pope Pius XI, 1933: “Now, Venerable Brothers and Beloved Sons, We cannot conclude Our letter better than by repeating that more than the help of men We must have confidence in the indefectible assistance promised by God to His Church and in the immense goodness of the Lord toward those who love Him.” (Dilectissima Nobis 26).
Pope Pius XI, 1929: “Upon this Magisterium, Christ the Lord conferred immunity from error, together with the command to teach His doctrine to all….” [Divini illius magistri, December 31, 1929; Denz. 2204.]
Pope Pius XII, 1943: “40. But we must not think that He rules only in a hidden or extraordinary manner. On the contrary, our Redeemer also governs His Mystical Body in a visible and normal way through His Vicar on earth. You know, Venerable Brethren, that after He had ruled the “little flock” Himself during His mortal pilgrimage, Christ our Lord, when about to leave this world and return to the Father, entrusted to the Chief of the Apostles the visible government of the entire community He had founded. Since He was all wise He could not leave the body of the Church He had founded as a human society without a visible head. Nor against this may one argue that the primacy of jurisdiction established in the Church gives such a Mystical Body two heads. For Peter in view of his primacy is only Christ’s Vicar; so that there is only one chief Head of this Body, namely Christ, who never ceases Himself to guide the Church invisibly, though at the same time He rules it visibly, through him who is His representative on earth. After His glorious Ascension into Heaven this Church rested not on Him alone, but on Peter, too, its visible foundation stone. That Christ and His Vicar constitute one only Head is the solemn teaching of Our predecessor of immortal memory Boniface VIII in the Apostolic Letter Unam Sanctam; and his successors have never ceased to repeat the same.
“41. They, therefore, walk in the path of dangerous error who believe that they can accept Christ as the Head of the Church, while not adhering loyally to His Vicar on earth. They have taken away the visible head, broken the visible bonds of unity and left the Mystical Body of the Redeemer so obscured and so maimed, that those who are seeking the haven of eternal salvation can neither see it nor find it.” [Mystici Corporis Christi]
Pope St. Paul VI, 1968: “founded upon the apostles and handing on from century to century their ever-living Word and their powers as Pastors in the successor of Peter and the bishops in communion with him; perpetually assisted by the Holy Spirit, She has the charge of guarding, teaching, explaining and spreading the Truth which God revealed in a then-veiled manner by the prophets, and fully by the Lord Jesus.” [Apostolic Letter Solemni Hac Liturgia]
Pope St. John Paul II, 1979: “She [the Church] was born on the cross on Good Friday — as the Fathers teach; She revealed this birth of Hers to the world on the day of Pentecost, when the Apostles were “clothed with power from on high” (Lk 24:49); when they were “baptized with the Holy Spirit” (Acts 1:5). “Ubi enim Ecclesia, ibi et Spiritus Dei; ubi Spiritus Dei, illic Ecclesia et omnis gratia: Spiritus autem veritas” (Where the Church is, there is also the Spirit of God; and where the Spirit of God is, there is the Church and all grace: the Spirit is truth.”) [Inner quote from St. Irenaeus, Against Heresies, II, 24, 1]”
Cardinal Ratzinger, CDF, 1990: “Divine assistance is also given to the successors of the apostles teaching in communion with the successor of Peter, and in a particular way, to the Roman Pontiff as Pastor of the whole Church, when exercising their ordinary Magisterium, even should this not issue in an infallible definition or in a ‘definitive’ pronouncement but in the proposal of some teaching which leads to a better understanding of Revelation in matters of faith and morals and to moral directives derived from such teaching.
“One must therefore take into account the proper character of every exercise of the Magisterium, considering the extent to which its authority is engaged. It is also to be borne in mind that all acts of the Magisterium derive from the same source, that is, from Christ who desires that His People walk in the entire truth. For this same reason, magisterial decisions in matters of discipline, even if they are not guaranteed by the charism of infallibility, are not without divine assistance and call for the adherence of the faithful.” [Donum Veritatis 17]
Cardinal Ratzinger, CDF, 1998: “Thus, in the early Christian communities, as later throughout the Church, the image of Peter remained fixed as that of the Apostle who, despite his human weakness, was expressly assigned by Christ to the first place among the Twelve and was called to exercise a distinctive, specific task in the Church. He is the rock on which Christ will build his Church; he is the one, after he has been converted, whose faith will not fail and who will strengthen his brethren; lastly, he is the Shepherd who will lead the whole community of the Lord’s disciples.”
“The Successor of Peter is the rock which guarantees a rigorous fidelity to the Word of God against arbitrariness and conformism: hence the martyrological nature of his primacy.”
“only the Pope (or the Pope with an Ecumenical Council) has, as the Successor of Peter, the authority and the competence to say the last word on the ways to exercise his pastoral ministry in the universal Church.” 
“The Catholic Church professes that this ministry is the primatial ministry of the Roman Pontiff, Successor of Peter, and maintains humbly and firmly ‘that the communion of the particular Churches with the Church of Rome, and of their Bishops with the Bishop of Rome, is — in God’s plan — an essential requisite of full and visible communion’…. We are all invited to trust in the Holy Spirit, to trust in Christ, by trusting in Peter.”
[The Primacy of the Successor of Peter in the Mystery of the Church]
Code of Canon Law, 1983:
Canon 751: “Heresy is the obstinate denial or obstinate doubt after the reception of baptism of some truth which is to be believed by divine and Catholic faith; apostasy is the total repudiation of the Christian faith; schism is the refusal of submission to the Supreme Pontiff or of communion with the members of the Church subject to him.”
Canon 1364, n. 1: “an apostate from the faith, a heretic, or a schismatic incurs a latae sententiae excommunication”
Can. 915 “Those who have been excommunicated or interdicted after the imposition or declaration of the penalty and others obstinately persevering in manifest grave sin are not to be admitted to holy communion.”
Canon Law 1373: “A person who publicly incites among subjects animosities or hatred against the Apostolic See or an ordinary because of some act of power or ecclesiastical ministry or provokes subjects to disobey them is to be punished by an interdict or other just penalties.”
“Can. 212 §1. Conscious of their own responsibility, the Christian faithful are bound to follow with Christian obedience those things which the sacred pastors, inasmuch as they represent Christ, declare as teachers of the faith or establish as rulers of the Church.”
Canon Law 1404: “The First See is judged by no one”
Ludwig Ott:, 2018, “It has been the constant teaching of the Catholic Church from the earliest times that the teachings of the General Councils are infallible.” Ott, The Fundamentals of Catholic Dogma Revised and Updated Edition (London: Baronius Press, 2018), p. 321.