I have never seen a screw head like the one attached. My local hardware store directed me to get different T heads (T6, T8, T10, T15, T20, T25) and try them until I find a match. None of them work though because as you can see from the picture, in the middle of the star there is a raised seed that prevents the driver from entering the head and engaging the star edges.
Looks like a "Tamper-Resistant Torx" screw, according to http://resources.tannerbolt.com/articles/what-type-of-screw-is-this/ . Another name is "Torx Security" screws. I get some good results on Amazon for Tamper Proof screws too.
Test what size was closest (diagonal fit) to get the approximate size you need. Probably the best action is to buy a whole set of interchangeable heads for your screwdriver.