I wouldn't take the list of Hippolytus, the first antiPope too seriously. All credible scholars and historians unanimously agree that St. Peter, appointed by Jesus, was the first Bishop of Rome and Pope.
****All credible scholars and historians unanimously agree that St. Peter, appointed by Jesus, was the first Bishop of Rome and Pope.****
If we wanted to get Technical and biblical, the first leader of the Church was James the Dirty (never bathed) of Jerusalem.
Even Peter feared him when Peter came from the conversion of Cornelius, and James made the decisions when St Paul went to Jerusalem to free the Gentiles from circumcision.