Right in the first chapter of 1 Corinthians, Paul responded to the troubling news that was sent to him from Chloe about how factions were developing among the Corinthian Christ believers. That is, in 1 Corinthians 1:12 we hear that different groups were claiming to be followers of either Paul, Apollos, or Cephas (i.e. Peter), with one group claiming to be morally superior to all the rest by professing their sole allegiance to Christ. Acts 18:24-19:1 describes Apollos as an Alexandrian Jew who was a learned exegete of Scripture and an enthusiastic preacher of Jesus, though apparently he only knew some preliminary details (e.g. “the baptism of John”) and had to be instructed more thoroughly by Paul’s co-workers Priscilla and Aquila, and that he ministered in Ephesus and Corinth. Was Apollos the real source of the division in Corinth? Perhaps Paul’s polemical remarks about mere human wisdom and rhetorically eloquent speech were partially directed at Apollos. In this case, Peter’s name could have been added to make the rhetorical point about the foolishness of aligning with one leader over another, when they were mere servants of the gospel (see 1 Cor 3:4-8, 22-23). On the other hand, perhaps Peter did make a trip to Corinth and a faction had formed there that claimed to be loyal to the mother church in Jerusalem. According to the bishop Dionysius of Corinth, Peter and Paul had planted the gospel in Corinth and Rome (Letter to Pope Soter, in Eusebius, Ecclesiastical History 2.25.8). If the latter is the case, that means that Peter was also a travelling missionary along with his wife (cf. 1 Cor 9:5) and strengthens the possibility that he moved from Corinth to Rome.
Peter in Rome: A Cephas Party in Corinth?