Subunit of clathrin-associated adaptor protein complex 1 that plays a role in protein sorting in the trans-Golgi network (TGN) and endosomes. The AP complexes mediate the recruitment of clathrin to membranes and the recognition of sorting signals within the cytosolic tails of transmembrane cargo molecules. Also involved in early steps of phagocytosis and macropinocytosis. Adaptor protein complex 1 (AP-1) is a heterotetramer composed of two large adaptins (gamma-type subunit and beta-type subunit), a medium adaptin (mu-type subunit) and a small adaptin (sigma-type subunit). Belongs to the adaptor complexes small subunit family.