What screwdriver I should use for this screw head?
It appears that the hex sides of that screw head have been rounded off due to the use of an ill-fitting hex wrench. A metric and an SAE hex wrench will both fit in there, but the use of the wrong one, while it feels like it fits properly, can be just loose enough that if the set screw is corroded in a bit, the wrench can slip and round over the edges.
You will need a screw extractor, like this:

Image courtesy of Lowes.com. No endorsement of brand or vendor intended or implied.
You insert this into a drill and run the drill in reverse. The extractor has a reverse thread that drills into the head of the screw and also turns the screw to back it out.
For the small added expense (and probably near impossibility of finding them individually), I'd suggest that you purchase a set of 3-5 extractors. That will help ensure you have the proper size for this screw, and you'll have a variety for future use. Note that these should work on nearly any screw with any type of screw head - slotted, Phillips, Torx, or other - not just the hex head of your set screw.
Once you have it out, you'll need to take it back to the hardware store/home-improvement center to buy an exact match (thread &amp; length) replacement. As much work as you put into getting it out, you don't want to reinsert it and have to do it again...