Finite simple groups acting with fixity 4 and their occurrence as groups of automorphisms of Riemann surfaces (extended version)

In previous work, all finite simple groups that act with fixity 4 have been classified. In this article we investigate which ones of these groups act faithfully on a compact Riemann surface of genus at least 2 with fixity four in total and in such a way that fixity 4 is exhibited on at least one orbit. This is an extended version of the submitted article, including our GAP code.