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.
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.
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.”
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]
Pope St. 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 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 St. Leo IX: “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, 1053; Denzinger 351-353.]
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, later confirmed by the Fifth Lateran Council:
“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]
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.]
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 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”
Categories: The Pope