Philemon is mentioned once in the letter named after him.
What we can gather from the New Testament itself is that he lived in Colossae.
There was a church there, which was likely founded by Ephaphras (See Col 1:7) and the church met at Philemon's house (See Philemon 2). Paul's Letter to the Colossian church was likely sent at the same time that the letter to Philemon was sent.
What we also know is that Philemon was a slaveowner and that his slave Onesimus had escaped. Paul's letter to Philemon was Paul's way of returning Onesimus to his master and to ask Philemon 1) not to punish Onesimus and 2) even more to look on Onesimus as as more than a slave but as a brother.
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very good answer!