Fusion systems related to polynomial representations of SL2(q)

Let (Formula presented.) be a power of a fixed prime (Formula presented.). We classify up to isomorphism all simple saturated fusion systems on a certain class of (Formula presented.) -groups constructed from the polynomial representations of (Formula presented.), which includes the Sylow (Formula presented.) -subgroups of (Formula presented.) and (Formula presented.) as special cases. The resulting list includes all Clelland–Parker fusion systems, a simple exotic fusion system discovered by Henke–Shpectorov, and a new infinite family of exotic examples.