There are more historical records to show that St. Peter was Bishop of Rome until he was martyred about 67.
Here are just a few...
Lactantius, The Deaths of the Persecutors 2:5, AD 318, "When Nero was already reigning, Peter came to Rome, where, in virtue of the performance of certain miracles which he worked . . . he converted many to righteousness and established a firm and steadfast temple to God. When this fact was reported to Nero . . . 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."
Bishop Peter of Alexandria, Penance, Canon 9, AD 306, "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."
Bishop Eusebius of Caesarea, The Chronicle, AD 303, "[In the second] year of the two hundredth and fifth Olympiad [AD 42]: The Apostle Peter, after he has established the church in Antioch, is sent to Rome, where he remains as a bishop of that city, preaching the gospel for twenty-five years."
The Poem Against the Marcionites, AD 267, "In this chair in which he himself had sat, Peter in mighty Rome commanded Linus, the first elected, to sit down."
St. Cyprian, Epistle 52, A. D. 251, described Rome as "The place of Peter."
Orien, Third Commentary on Genesis, AD 232, quoted by Bishop Eusebius in Church History, "Peter…at last, having come to Rome, he was crucified head-downwards; for he had requested that he might suffer this way."
The Little Labyrinth, AD 211, quoted by Bishop Eusebius in Church History 5:28:3, "Victor . . . was the thirteenth bishop of Rome from Peter."
Tertullian, Against Marcion 4, 5:1, AD 210, "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."
Tertullian, Demurrer Against the Heretics 36 and 32:2, AD 200, "But if you are near Italy, you have Rome, where authority is at hand for us too. What a happy church that is, on which the apostles poured out their whole doctrine with their blood; where Peter had a passion like that of the Lord, where Paul was crowned with the death of John [the Baptist, by being beheaded]…[T]his is the way in which the apostolic churches transmit their lists: like the church of the Smyrneans , which records that Polycarp was placed there by John, like the church of the Romans, where Clement was ordained by Peter."
Clement of Alexandria, Sketches, AD 200, quoted by Bishop Eusebius in Church History 6, 14:1, "The circumstances which occasioned . . . [the writing] of Mark were these: 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 a long time his follower and who remembered his sayings; should write down what had been proclaimed."
Caius, Disputation with Proclus, AD 198, quoted by Bishop Eusebius in Church History 2:25:5, "It is recorded that Paul was beheaded in Rome itself, and Peter, likewise, was crucified, during the reign [of the Emperor Nero]. The account is confirmed by the names of Peter and Paul over the cemeteries there, which remain to the present time. And it is confirmed also by a stalwart man of the Church, Caius by name, who lived in the time of Zephyrinus, Bishop of Rome. This Caius, in a written disputation with Proclus, the leader of the sect of Cataphrygians, says this of the places in which the remains of the aforementioned apostles were deposited: ‘I can point out the trophies of the apostles. For if you are willing to go to the Vatican or to the Ostian Way, you will find the trophies of those who founded this Church’."
St. Irenaeus, Bishop of Lyons, Against Heresies 3:3:1, 3:3:2, and 3:3:3, AD 189, "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.
"But since it would be too long to enumerate in such a volume as this the succession 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. With that church, because of its superior origin, all the 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.
"The blessed apostles [Peter and Paul], having founded and built up the church [of Rome], they handed over the office of the episcopate to Linus. Paul makes mention of this Linus in the letter to Timothy. To him succeeded Anacletus, and after him, in the third place from the apostles, Clement was chosen for the episcopate. He had seen the blessed apostles and was acquainted with them. It might be said that he still heard the echoes of the preaching of the apostles and had their traditions before his eyes. And not only he, for there were many still remaining who had been instructed by the apostles. In the time of Clement, no small dissension having arisen among the brethren in Corinth, the Church in Rome sent a very strong letter to the Corinthians, exhorting them to peace and renewing their faith . . . To this Clement, Evaristus succeeded . . . and now, in the twelfth place after the apostles, the lot of the episcopate [of Rome] has fallen to Eleutherus. In this order, and by the teaching of the apostles handed down in the Church, the preaching of the truth has come down to us."
St. Dionysius, Bishop of Corinth, Letter to Pope Soter, AD 170, quoted by Bishop Eusebius in Church History 2:25:8, "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."
St. Ignatius, Bishop of Antioch, while being brought to Rome for martyrdom, wrote Letter to the Romans 4:3, AD 110, "I issue you no commands, like Peter and Paul: they were Apostles, while I am but a captive."
Pope Clement (fourth Bishop of Rome), First Epistle to the Corinthians, Chapter 5, AD 96, "But not to dwell upon ancient examples, let us come to the most recent spiritual heroes. Let us take the noble examples furnished in our own generation. Through envy and jealousy, the greatest and most righteous pillars [of the Church] have been persecuted and put to death. Let us set before our eyes the illustrious apostles. Peter, through unrighteous envy, endured not one or two, but numerous labours, and when he had finally suffered martyrdom, departed to the place of glory due to him. Owing to envy, Paul also obtained the reward of patient endurance, after being seven times thrown into captivity, compelled to flee, and stoned. After preaching both in the east and west, he gained the illustrious reputation due to his faith, having taught righteousness to the whole world, and come to the extreme limit of the west, and suffered martyrdom under the prefects. Thus was he removed from the world, and went into the holy place, having proved himself a striking example of patience."
There are more historical records to show that St. Peter was Bishop of Rome until he was martyred about 67