Fusion rules for the orbifold vertex operator algebras $L_{\widehat{{\mathfrak{s}\mathfrak{l}}_2}}(k,0{)}^K$

For the Klein group $K$ and a positive integr $k$, irreducible modules of the orbifold vertex operator algebra $L_{\widehat{{\mathfrak{s}\mathfrak{l}}_2}}(k,0{)}^K$ have been classified and constructed in \cite{JWa}. In this paper, we determine completely the fusion rules of $L_{\widehat{{\mathfrak{s}\mathfrak{l}}_2}}(k,0{)}^K$.