Albert Barnes on Philemon 1:17

If thou count me therefore a partner. The word rendered partner, (κοινωνος,) means a partaker, a companion. The idea in the word is that of having something in common (κοινος) with any one --as common principles; common attachments; a common interest in an enterprise; common hopes. It may be applied to those who hold the same principles of religion, and who have the same hope of heaven, the same views of things, etc. Here the meaning is, that if Philemon regarded Paul as sharing with him in the principles and hopes of religion, or as a brother in the gospel, so that he would receive him, he ought to receive Onesimus in the same way. He was actuated by the same principles, and had the same hopes, and had a claim to be received as a Christian brother. His receiving Onesimus would be interpreted by Paul as proof that he regarded him as a partaker of the hopes of the gospel, and as a companion and friend. For a plea in behalf of another, strongly resembling this, see Horace, Epis. Lib. 1, Ep. 9.

(a) "partner" 2Cor 8:23