Coset construction and orbifold construction are two important ways to construct new VOAs from given ones. Parafermion VOA is a special kind of coset construction related to the affine VOA. In this talk, first I will present the classification of irreducible modules and fusion rules for the $\mathbb{Z}_{2}$-orbifold of the affine VOA of type $A_{1}^{(1)}$. Then I will explain how to classify the irreducible modules of the $\mathbb{Z}_{2}$-orbifold of the parafermion VOA of type $A_{1}^{(1)}$ and determine their fusion rules by applying the results of the $\mathbb{Z}_{2}$-orbifold of the affine VOA. These results are based on the joint works with Cuipo Jiang.