Where was the Apostle Peter crucified?

Answer 1

Tradition tells us that Peter was crucified upside down in Rome.
The only verified document to survive from the reign of Pope Clement was his first letter to the Corinthians. The purpose of the letter was to admonish some members of the Church there for their bad behavior. The reason Peter in Rome isn't mention is because that was not the intention nor the focus of Clement's letter to the Church in Corinth. As to Anicetus, virtually nothing is known about his papacy and no writings of his survive so the statement concerning the beheading of Peter must be taken as a pious legend. His discussion was with St. Polycarp concerning the fixing of the date that Easter was to be celebrated.

Answer 2

There is no good reason to suppose that the apostle Peter was crucified at all. Clement of Rome, writing around 95 CE (1 Clement), spoke in general terms about the life and death of Peter but appears to have been unaware that Peter had even visited Rome and was certainly unaware that he had been executed in any way at all, although he surely would have known if this were the case.

During the second century, Pope Anicetus, wishing to demonstrate that he spoke with the authority of Peter, reported that Peter had been beheaded in Rome. Then, a century later, Origen changed this to say that Peter was sentenced to crucifixion but, feeling unworthy of being crucified like Jesus, asked to be crucified upside down. Although this is pious midrash, it says that Peter was crucified in Rome.