9 PCS Countersink Drill Bits Set, 5PCS Two-Flute TCT Alloy Tapered Drill Bits and Adjustable Depth Stop Collar, Wood Countersink Bit with Wrench for 82 Degree Woodworking, Plywood and MDF DIY

Put a plant in front of them. No, jk. The answer is in here. Remove the screw you have. Redrill with a countersink bit that will make a counterbore (so the screw head is below the surface and you have a straight hole several mm deep). Drive your screw and plug. These types of countersink bits make a hole that fits a 3/8" dowel. You can buy plugs, make them from a matching piece of hardwood with a plug cutter bit or just buy a length of 3/8 dowel, glue it in and use an inexpensive flush cutting saw to trim it flush and sand. Bit Flush Cut Saw