Rational torsion points on abelian surfaces with quaternionic multiplication

Let A be an abelian surface over whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur's theorem for elliptic curves, we show that the torsion subgroup of is -torsion and has order at most. Under the additional assumption that A is of -type, we give a complete classification of the possible torsion subgroups of.