  Quaternionic Shimura surfaces are quotient of the bidisc by an irreducible
cocompact arithmetic group. In the present paper we are interested in (smooth)
quaternionic Shimura surfaces admitting an automorphism with one dimensional
fixed locus; such automorphisms are involutions. We propose a new construction
of surfaces of general type with $q=p_{g}=0$ as quotients of quaternionic
Shimura surfaces by such involutions. These quotients have finite fundamental
group.
