In this article we construct three \textit{q}-King type operators which fix the functions $e_0$ and $e_2+\alpha e_1$, $\alpha>0$. We study the rates of convergence for the iterates of these operators using the first and the second order modulus of continuity. We show that the convergence is faster in the case of \textit{q} operators ($q<1$) than in the classical case ($q=1$).