Php 4:3 - Yes, and I ask you, loyal yokefellow, help these women who have contended at my side in the cause of the gospel, along with Clement and the rest of my fellow workers, whose names are in the book of life.
Clement had been a companion of Paul and the Corinthians were familiar with him through the word of Paul as a man of faith. Clement was a Roman in Philippi, and he had the commendation of Paul, so it is no wonder that the Corinthian church founded by Paul would seek the advice of a man with Pauline approval. Philippi sent help via Epaphroditus while Paul was imprisoned in Rome, so the pattern of appealing to what was Pauline was evident in the churches Paul had founded. So with the Corinthians. It would be natural to inquire of a trusted friend of Paul for advice.
I'm curious as to how we can say that Clement a) was a Roman in Philippi and b) was the companion of Paul.
The reason I say that is that all the accounts I've read (and some of them are apocryphal, so using them with appropriate cautiousness) say that Clement was the companion of Peter in the East--not Paul.
The way I read Philippians 4, Clement is right there in Rome with Paul...and I don't know of any evidence that Clement was together with Paul anywhere outside that city.
I'm heavily researching this era right now, so any scrap of information you have would prove helpful. I've already gone through all the Clementine literature.