The claim that Peter was in Rome in the time of Claudius is certainly unhistorical, was it introduced by Eusebius ?
I'm posting a lot of notes so I can see what there is to see about Peter being in Rome. I've been looking over this question, and to me it looks like it boils down to Simon Magus, and the earliest Christian reference to him is in Acts 8:9-25:
Now for some time a man named Simon had practiced sorcery in the city and amazed all the people of Samaria. He boasted that he was someone great, and all the people, both high and low, gave him their attention and exclaimed, “This man is rightly called the Great Power of God.” They followed him because he had amazed them for a long time with his sorcery. But when they believed Philip as he proclaimed the good news of the kingdom of God and the name of Jesus Christ, they were baptized, both men and women. Simon himself believed and was baptized. And he followed Philip everywhere, astonished by the great signs and miracles he saw.
When the apostles in Jerusalem heard that Samaria had accepted the word of God, they sent Peter and John to Samaria. When they arrived, they prayed for the new believers there that they might receive the Holy Spirit, because the Holy Spirit had not yet come on any of them; they had simply been baptized in the name of the Lord Jesus. Then Peter and John placed their hands on them, and they received the Holy Spirit.
When Simon saw that the Spirit was given at the laying on of the apostles’ hands, he offered them money and said, “Give me also this ability so that everyone on whom I lay my hands may receive the Holy Spirit.”
Peter answered: “May your money perish with you, because you thought you could buy the gift of God with money! You have no part or share in this ministry, because your heart is not right before God. Repent of this wickedness and pray to the Lord in the hope that he may forgive you for having such a thought in your heart. For I see that you are full of bitterness and captive to sin.”
Then Simon answered, “Pray to the Lord for me so that nothing you have said may happen to me.”
After they had further proclaimed the word of the Lord and testified about Jesus, Peter and John returned to Jerusalem, preaching the gospel in many Samaritan villages.
Since I think Luke/Acts used Josephus, I'm thinking this is the same Simon Josephus mentions in Ant. 20.7.2:
2. But for the marriage of Drusilla with Azizus, it was in no long time afterward dissolved upon the following occasion: While Felix was procurator of Judea, he saw this Drusilla, and fell in love with her; for she did indeed exceed all other women in beauty; and he sent to her a person whose name was Simon one of his friends; a Jew he was, and by birth a Cypriot, and one who pretended to be a magician, and endeavored to persuade her to forsake her present husband, and marry him; and promised, that if she would not refuse him, he would make her a happy woman. Accordingly she acted ill, and because she was desirous to avoid her sister Bernice's envy, for she was very ill treated by her on account of her beauty, was prevailed upon to transgress the laws of her forefathers, and to marry Felix; and when he had had a son by her, he named him Agrippa. But after what manner that young man, with his wife, perished at the conflagration of the mountain Vesuvius, in the days of Titus Caesar, shall be related hereafter.
I gather that Simon Magus is thought to have been a Samaritan and thus could not be Josephus' Simon (whom he says was Jewish), but I don't see anything in Acts 8 above that suggests Simon was a Samaritan, only that he preached to Samaritans in addition to people in Jerusalem ("A man named Simon had practiced sorcery in the city and amazed all the people of Samaria"). And the key that this is Josephus' Simon is "and all the people, both high and low, gave him their attention," which fits what Josephus says about his Simon, that he had, "endeavored to persuade her [Drusilla] to forsake her present husband, and marry him [Felix]." This at least covers the "high" part of the "high and low" of "all the people" (which included, I presume, people in Jerusalem, like Felix and Drusilla) whom Acts says gave their attention to him.
The next thing seems to be the Acts of Peter (c. 150-200 CE), which places Simon Magus in Rome and has Peter confront him there.
Around the same time, Irenaeus is the first person I'm aware of who interprets Acts 8 to mean that Simon was a Samaritan (AH 1.23.1), but in any event it is an interpretation I don't agree with. And while he doesn't appear to mention Rome, Irenaeus says that Simon was active during the time of Claudius, though without naming a source other than "he is said," which I assume refers to the Acts of Peter ("Such was his procedure in the reign of Claudius Cæsar, by whom also he is said
to have been honoured with a statue, on account of his magical power").
Acts of Peter: "I set up a statue to him with this inscription: 'To Simon the new (young) God.'"
So I'm thinking that the Simon in Acts is based on the Simon in Josephus, and that both of them are Jewish and not Samaritan, and that Irenaeus interprets Acts to mean that he was a Samaritan, and that Irenaeus' statement that Simon was active in the time of Claudius is based on the Acts of Peter.
Okay, now we come to Eusebius, who I suppose could be dependent on Irenaeus and/or the Acts of Peter for the information that Simon was active during Claudius' time, but appears to not give any sources for it and gives what to me are very fanciful reasons for it (e,g, as a battle between "the evil power" that inspired Simon and "that divine and celestial grace" that inspired Peter).
1. The evil power, who hates all that is good and plots against the salvation of men, constituted Simon at that time the father and author of such wickedness, as if to make him a mighty antagonist of the great, inspired apostles of our Saviour.
2. For that divine and celestial grace which co-operates with its ministers, by their appearance and presence, quickly extinguished the kindled flame of evil, and humbled and cast down through them “every high thing that exalted itself against the knowledge of God.” 2 Corinthians 10:5
3. Wherefore neither the conspiracy of Simon nor that of any of the others who arose at that period could accomplish anything in those apostolic times. For everything was conquered and subdued by the splendors of the truth and by the divine word itself which had but lately begun to shine from heaven upon men, and which was then flourishing upon earth, and dwelling in the apostles themselves.
4. Immediately the above-mentioned impostor was smitten in the eyes of his mind by a divine and miraculous flash, and after the evil deeds done by him had been first detected by the apostle Peter in Judea, he fled and made a great journey across the sea from the East to the West, thinking that only thus could he live according to his mind.
5. And coming to the city of Rome, by the mighty co-operation of that power which was lying in wait there, he was in a short time so successful in his undertaking that those who dwelt there honored him as a god by the erection of a statue.
6. But this did not last long. For immediately, during the reign of Claudius, the all-good and gracious Providence, which watches over all things, led Peter, that strongest and greatest of the apostles, and the one who on account of his virtue was the speaker for all the others, to Rome against this great corrupter of life. Clad in divine armor like a noble commander of God, He carried the costly merchandise of the light of the understanding from the East to those who dwelt in the West, proclaiming the light itself, and the word which brings salvation to souls, and preaching the kingdom of heaven.
And though he doesn't give any sources, it sounds to me like he put Irenaeus and the Acts of Peter together to craft the above story.
I think we're on firmer ground regarding Peter being in Rome during the time of Nero
and being martyred there by what Eusebius says in EH 2.25.1-8, where he provides several sources for it:
1. When the government of Nero was now firmly established, he began to plunge into unholy pursuits, and armed himself even against the religion of the God of the universe.
2. To describe the greatness of his depravity does not lie within the plan of the present work. As there are many indeed that have recorded his history in most accurate narratives, every one may at his pleasure learn from them the coarseness of the man's extraordinary madness, under the influence of which, after he had accomplished the destruction of so many myriads without any reason, he ran into such blood-guiltiness that he did not spare even his nearest relatives and dearest friends, but destroyed his mother and his brothers and his wife, with very many others of his own family as he would private and public enemies, with various kinds of deaths.
3. But with all these things this particular in the catalogue of his crimes was still wanting, that he was the first of the emperors who showed himself an enemy of the divine religion.
4. The Roman Tertullian is likewise a witness of this. He writes as follows: “Examine your records. There you will find that Nero was the first that persecuted this doctrine, particularly then when after subduing all the east, he exercised his cruelty against all at Rome. We glory in having such a man the leader in our punishment. For whoever knows him can understand that nothing was condemned by Nero unless it was something of great excellence.”
5. Thus publicly announcing himself as the first among God's chief enemies, he was led on to the slaughter of the apostles. It is, therefore, recorded that Paul was beheaded in Rome itself, and that Peter likewise was crucified under Nero. This account of Peter and Paul is substantiated by the fact that their names are preserved in the cemeteries of that place even to the present day.
6. It is confirmed likewise by Caius, a member of the Church, who arose under Zephyrinus, bishop of Rome. He, in a published disputation with Proclus, the leader of the Phrygian heresy, speaks as follows concerning the places where the sacred corpses of the aforesaid apostles are laid:
7. “But I can show the trophies of the apostles. For if you will go to the Vatican or to the Ostian way, you will find the trophies of those who laid the foundations of this church.”
8. And that they both suffered martyrdom at the same time is stated by Dionysius, bishop of Corinth, in his epistle to the Romans, in the following words: “You have thus by such an admonition bound together the planting of Peter and of Paul at Rome and Corinth. For both of them planted and likewise taught us in our Corinth. And they taught together in like manner in Italy, and suffered martyrdom at the same time.” I have quoted these things in order that the truth of the history might be still more confirmed.
So I don't think that Peter was in Rome during the time of Claudius, but he perhaps could have been there during Nero's time, and his confrontation with Simon Magus there seems to be based on the Acts of Peter (whatever that is worth).
You know in spite of all you gained, you still have to stand out in the pouring rain.