Dionysius of Corinth
You have also, by your very admonition, brought together the planting that was made by Peter and Paul at Rome and at Corinth; for both of them alike planted in our Corinth and taught us; and both alike, teaching similarly in Italy, suffered martyrdom at the same time (Letter to Soter of Rome [inter A.D. 166 -174] as recorded by Eusebius).
Matthew also issued among the Hebrews a written Gospel in their own language, while Peter and Paul were evangelizing in Rome and laying the foundation of the Church. After their departure, Mark, the disciple and interpreter of Peter, also handed down to us in writing what had been preached by Peter (Against Heresies 3:1:1 [A.D. 189]).
But since it would be too long to enumerate in such a volume as this the successions of all the Churches, we shall confound all those who, in whatever manner, whether through self-satisfaction or vainglory, or through blindness and wicked opinion, assemble other than where it is proper, by pointing out here the successions of the bishops of the greatest and most ancient Church known to all, founded and organized at Rome by the two most glorious Apostles, Peter and Paul, that Church which has the tradition and the faith which comes down to us after having been announced to men by the Apostles. For with this Church, because of its superior origin, all Churches must agree, that is, all the faithful in the whole world; and it is in her that the faithful everywhere have maintained the Apostolic tradition (Against Heresies 3:3:2 [A.D. 189]).
Let us see what milk the Corinthians drained from Paul; against what standard the Galatians were measured for correction; what the Philippians, Thessalonians, and Ephesians read; what even the nearby Romans sound forth, to whom both Peter and Paul bequeathed the Gospel and even sealed it with their blood (Against Marcion 4:5:1 [inter A.D. 207-212]).
The Apostle Peter, after he has established the Church in Antioch, is sent to Rome, where he remains bishop of that city, preaching the Gospel for twenty-five years (The Chronicle, Ad An. Dom. 42 [A.D. 303]).
When Peter preached the Word publicly at Rome, and declared the Gospel by the Spirit, many who were present requested that Mark, who had been for a long time his follower and who remembered his sayings, should write down what had been proclaimed. Having composed the Gospel, he gave it to those who had requested it (Ecclesiastical History 6:14:1 [A.D. 325]).
Peter of Alexandria
Peter, the first chosen of the Apostles, having been apprehended often and thrown into prison and treated with ignominy, at last was crucified in Rome (Canonical Letter, canon 9 [A.D. 306]).
When Nero was already reigning Peter came to Rome, where, in virtue of the performance of certain miracles which he worked by that power of God which had been given to him, he converted many to righteousness and established a firm and steadfast temple to God. When this fact was reported to Nero, he noticed that not only at Rome but everywhere great multitudes were daily abandoning the worship of idols, and, condemning their old ways, were going over to the new religion. Being that he was a detestable and pernicious tyrant, he sprang to the task of tearing down the heavenly temple and of destroying righteousness. It was he that first persecuted the servants of God. Peter, he fixed to a cross; and Paul, he slew (The Deaths of the Persecutors 2:5 [inter A.D. 316-320]).
Cyril of Jerusalem
[Simon Magus] so deceived the City of Rome that Claudius erected a statue of him, and wrote beneath it in the language of the Romans Simoni Deo Sancto, which is translated To the Holy God Simon. While the error was extending itself Peter and Paul arrived, a noble pair and the rulers of the Church; and they set the error aright… for Peter was there, he that carries about the keys of heaven (Catechetical Lectures 6:14 [A.D. 350]).
The first see, therefore, is that of Peter the Apostle, that of the Roman Church, which has neither stain nor blemish nor anything like it. The second see, however, is that at Alexandria, consecrated in behalf of blessed Peter by Mark, his disciple and an evangelist, who was sent to Egypt by the Apostle Peter, where he preached the word of truth and finished his glorious martyrdom. The third honorable see, indeed, is that at Antioch, which belonged to the most blessed Apostle Peter, where first he dwelt before he came to Rome, and where the name Christians was first applied, as to a new people (The Decree of Damasus 3 [A.D. 382]).