  This paper is about the orbifold theory of parafermion vertex operator
algebras $K(osp(1|2),k)$ associated to the affine vertex operator superalgebra
$L_{\widehat{osp(1|2)}}(k,0)$ with any positive integer $k$. Among the main
results, we classify the irreducible modules for the orbifold of parafermion
vertex operator algebra $K(osp(1|2),k)$.
