A.T. Robertson Commentary Philemon 1:13

"whom I would fain have kept with me, that in thy behalf he might minister unto me in the bonds of the gospel:" — Philemon 1:13 (ASV)

I would fain have kept (εβουλομην κατεχειν). Imperfect middle and present infinitive, "I was wishing to hold back." Again from the standpoint of the arrival of Onesimus.

In thy behalf (υπερ σου). So "in thy stead," "in place of thee."

He might minister (διακονη). Present active subjunctive (retained after εβουλομην) with ινα, purpose continued, "that he might keep on ministering."