St. Jerome
"[Pope] Stephen . . . was the blessed Peter�s twenty-second successor in the See of Rome" (Against the Luciferians 23 [A.D. 383]).
"Clement, of whom the apostle Paul writing to the Philippians says �With Clement and others of my fellow-workers whose names are written in the book of life,� the fourth bishop of Rome after Peter, if indeed the second was Linus and the third Anacletus, although most of the Latins think that Clement was second after the apostle" (Lives of Illustrious Men 15 [A.D. 396]).
"Since the East, shattered as it is by the long-standing feuds, subsisting between its peoples, is bit by bit tearing into shreds the seamless vest of the Lord . . . I think it my duty to consult the chair of Peter, and to turn to a church [Rome] whose faith has been praised by Paul [Rom. 1:8]. I appeal for spiritual food to the church whence I have received the garb of Christ. . . . Evil children have squandered their patrimony; you alone keep your heritage intact" (Letters 15:1 [A.D. 396]).
...
"I follow no leader but Christ and join in communion with none but your blessedness [Pope Damasus I], that is, with the chair of Peter. I know that this is the rock on which the Church has been built. Whoever eats the Lamb outside this house is profane. Anyone who is not in the ark of Noah will perish when the flood prevails" (ibid., 15:2).
"The church here is split into three parts, each eager to seize me for its own. . . . Meanwhile I keep crying, �He that is joined to the chair of Peter is accepted by me!� . . . Therefore, I implore your blessedness [Pope Damasus I] . . . tell me by letter with whom it is that I should communicate in Syria" (ibid., 16:2).
Ambrose of Milan
"[T]hey [the Novatian heretics] have not the succession of Peter, who hold not the chair of Peter, which they rend by wicked schism; and this, too, they do, wickedly denying that sins can be forgiven [by the sacrament of confession] even in the Church, whereas it was said to Peter: �I will give unto thee the keys of the kingdom of heaven, and whatsoever thou shalt bind on earth shall be bound also in heaven, and whatsoever thou shall loose on earth shall be loosed also in heaven�[Matt. 16:19]" (Penance 1

33 [A.D. 388]).
St. Augustine
"If all men throughout the world were such as you most vainly accuse them of having been, what has the chair of the Roman church done to you, in which Peter sat, and in which Anastasius sits today?" (Against the Letters of Petilani 2:118 [A.D. 402]).
"If the very order of episcopal succession is to be considered, how much more surely, truly, and safely do we number them from Peter himself, to whom, as to one representing the whole Church, the Lord said, �Upon this rock I will build my Church� . . . [Matt. 16:18]. Peter was succeeded by Linus, Linus by Clement, Clement by Anacletus, Anacletus by Evaristus . . . " (Letters 53

2 [A.D. 412]).
Council of Ephesus
"Philip the presbyter and legate of the Apostolic See said: �There is no doubt, and in fact it has been known in all ages, that the holy and most blessed Peter, prince and head of the apostles, pillar of the faith, and foundation of the Catholic Church, received the keys of the kingdom from our Lord Jesus Christ, the Savior and Redeemer of the human race, and that to him was given the power of loosing and binding sins: who down even to today and forever both lives and judges in his successors. The holy and most blessed pope Celestine, according to due order, is his successor and holds his place, and us he sent to supply his place in this holy synod�" (Acts of the Council, session 3 [A.D. 431]).
Pope Leo I
"As for the resolution of the bishops which is contrary to the Nicene decree, in union with your faithful piety, I declare it to be invalid and annul it by the authority of the holy apostle Peter" (Letters 110 [A.D. 445]).
"Whereupon the blessed Peter, as inspired by God, and about to benefit all nations by his confession, said, �You are the Christ, the Son of the living God.� Not undeservedly, therefore, was he pronounced blessed by the Lord, and derived from the original Rock that solidity which belonged both to his virtue and to his name [Peter]" (The Tome of Leo [A.D. 449]).
Peter Chrysologus
"We exhort you in every respect, honorable brother, to heed obediently what has been written by the most blessed pope of the city of Rome, for blessed Peter, who lives and presides in his own see, provides the truth of faith to those who seek it. For we, by reason of our pursuit of peace and faith, cannot try cases on the faith without the consent of the bishop of Rome" (Letters 25:2 [A.D. 449]).
Council of Chalcedon
"After the reading of the foregoing epistle [The Tome of Leo], the most reverend bishops cried out: �This is the faith of the fathers! This is the faith of the apostles! So we all believe! Thus the orthodox believe! Anathema to him who does not thus believe! Peter has spoken thus through Leo! . . . This is the true faith! Those of us who are orthodox thus believe! This is the faith of the Fathers!�" (Acts of the Council, session 2 [A.D. 451]).