The goal of this paper is to construct a general class of operators which has known Baskakov-Schurer-Szász that preserving constant and e2ax,a > 0 functions. Also, we demonstrate the fact that for these operators, moments can be obtained using the concept of moment generating function. Furthermore, we investigate a uniform convergence result and a quantitative estimate in consideration of given operator, as well. Finally, we discuss the convergence of corresponding sequences in exponential weighted spaces and make a comparison about which one approximates better between classical Baskakov-Schurer-Szász operators and the recent sequence, too.