Clement’s First Epistle to the Corinthians is genuine, written in the 90’s AD. The second one, attributed to him, there is good evidence to believe was not his own. But even that evidence points to a date of about AD 150. It is still useful for the purpose of this discussion, though, since, with such a still relatively early provenience, it is a witness to the already accepted tradition of only 50 years earlier.
But, even apart from Clement, there is a lot of early evidence that Peter’s protracted ministry in Rome and his martyrdom there were universally understood and accepted. Is St. Irenaeus merely a Roman stooge in Against Heresies 3? Is Tertullian merely ignorant when he talks about Clement’s ordination by Peter in Rome? Does Cyprian know what he’s talking about when he states baldy that it was upon Peter that Christ built His Church? Does Pope Victor know what a troglodyte he was when he threw his weight around the universal Church, as Bishop of Rome, during the Quartodeciman controversy?
Look, the primacy of Peter is Christ-established and disciple-confirmed. It is an ecclesiastical exercise in revisionist history to claim that no one in the early Church had any notions of papal primacy until Gregory the Great came along. Sure, that primacy has been used in a heavy-handed manner form time to time, but the principle of its existence is pefectly valid. Thank God that the Church had a visible head amid all of the heresies promulgated, primarily in the East, in the patristic age!
It seems to me that you must belong to a brand of eastern Orthodoxy that likes the trappings of a liturgical Church, but is so hell-bent on denying the legitimacy of Rome’s claims that it must deny much of the early writings and traditions at the same time. Orthodoxy, like Catholicism, finds much of its roots in the early patristic writings. Don’t ignore the legitimacy of many of the early Fathers just to score spurious talking points against Rome.
Rome’s Pre-eminence has never been questioned. That the Patriarch of Rome had any authority outside of his jurisdiction is what Orthodoxy disputes. He NEVER had any authority outside of his own territory, unless it was to settle a dispute, which was done on more than one occasion, historically. The only entity with the power tomake decisions regarding doctrine and dogma are the Ecumenical Councils of the undivided Church. If Clement was genuine, or needed, then WHY was his First Epistle not added to the canon of scripture?