I doubt that there's anything to "Repair". If any headphone works in it, the jack is working and all the wires are connected. And that's about all that can be "repaired".
It's possible that some cheap headphones have such low sensitivity that you won't hear anything on them from a phone. Or that some of them have 2.5mm plugs (phones have 3.5mm jacks, so you need headphones with 3.5mm plugs - that's the diameter of the shaft of the part that plugs in). Or it could be other things.
Knowing what brands or types don't work might help us guess at the problem. But I've used cheapie (99 cents from the dollar store) headphones, Apple headphones, headphones running from $5 to $35 and in between, and aside from the differing volume levels, they all worked. (Some of the dollar store junk had the best sound. The old Apples were really comfortable and sounded good, but the price was ridiculous if I could get the same thing for $5 in a different brand.)
