  The aim of this paper is to determine minimal models of the semi-isogenous
mixed surfaces with $\chi=1$ and $K^2>0$ constructed by Cancian and Frapporti.
In order to do this, we further develop the idea of orbit divisors introduced
by Frapporti and Lee, to construct effective divisors on surfaces isogenous to
a product of mixed type, extending it to the semi-isogenous mixed surfaces.
