How do I fix a stripped screw on a cabinet hinge?

If I’m reading correctly, the problem is with where the hinge attaches to the wood.
The wood putty will work if you do it right.

Pack the hole with the wood putty. Use a toothpick to get it in the hole so that there are no voids. Smooth the surface while it’s still wet. This’ll save clean up time later.

Let it completely dry - A full day or so.

Once it’s dry, pre-drill the hole for the screw. Use a drll bit that’s the same size as the shank of the screw (slightly smaller than the width of the threads).

You can also try using a slightly longer screw. Make sure it’s not so long that it goes through and hits something though.

You need to ge to Lowes, Home Depot or your local hardware store and get some drywall anchors.

In the anchor department you will find a variety of anchors find one with the same size screw as the one in you cabinet (same diameter not length).

Then drill out the hole to the proper size of the anchor plug and drive it in with a hammer. Remount the door with the new screws and you are all set.

Good luck

Go and get a small plastic plug that you put in holes for hanging pictures on drywall. This might be a solution. If your thinking the top of the plastic head might be to big just file it down. hope this helps.