This article presents a new sequence of Gamma-type operators that retains the test function $e_r(t)=t^r$, $r\in\mathbb{N}$. Initially, we derive the moment formulas for these operators. Later, we analyze the approximation properties using the standard and weighted modulus of smoothness and prove an asymptotic Voronovskaja-type theorem. Furthermore, we compare the convergence rate and error estimation of the proposed operators with existing ones that preserve test functions in various ways, using numerical examples.