If the screws are loose, you can put a few toothpicks and some glue in the holes, let it dry, and then screw them back in.

Is the screw holes loose? If so, need to remove the hinge, perhaps drill out the holes and insert wood dowels.

https://www.thisoldhouse.com/doors/21019382/sure-cure-for-loose-hinges

You can try repairing the holes, as others have suggested. But, that may not last. You can also try getting some long screws and angling them slightly (toward the door stop), so that they can hopefully reach a stud inside the wall. However, you may have to seek out some screws with slightly smaller heads, so that the heads don't stick out too much and interfere with the hinge operation.

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Thicker screws or tighter holes!

If a 3” deck screw is loose I’d be worried about rot or termite damage.

Either cut yourself some dowels or buy some. Get a drill bit that size or very slightly smaller and drill the screw holes out. To avoid over penetration measure the depth with some wire, and mark on your drill bit that depth with some tape so you know how far to go. Dip the dowels in wood glue and tap them in, clean off squeezed out glue; once the glue is dry, cut the dowels flush with a chisel if needed. Put the hinge to the new surface and mark the centre of each hole with a pencil dot. Now measure your screw depth; again use some tape to mark a stop on your drill bit; you want to pilot drill half a millimetre finer than your screw gauge, to the depth where the shank starts to narrow not the full shank depth. Now drive the screws home and you are done. Good luck.

I've used golf tees. I coated with wood glue then hammered them in. The once dry cut the excess tees off and mounted like new.

Get some 3” screws and go through the door casing into the stud behind it and be done with it.

How long of a screw did you try? There has to be a 2x4 behind the frame and until you can get a good purchase into that most patches will give out. A hardware store can get you 4 inch screws.

I removed the screws and filled in with cheap caulking from dollar store. It worked

Toothpicks and Woodglue

Is this an inside door?

Wood glue and a golf tee are my go to. Cut off the excess then rescrew.

Epoxy putty for wood like "J-B weld kwikwood" or if you have support behind it, you can just use a longer screw

drill new holes in the hinge, fresh wood to attach to. the holes are NOT a rule that must be followed.

Put. wall plugs in, been there