<p>Szász–Mirakyan operators constitute an important class of positive linear operators in approximation theory due to their ability to approximate continuous functions on unbounded intervals. Motivated by the search for operators with improved approximation behaviour, we introduce a modified form of the classical Szász–Mirakyan operators and investigate their fundamental properties. We first establish the connection between the proposed operators and the classical Szász–Mirakyan operators and derive the corresponding moments. Using tools of classical approximation theory, including the modulus of continuity and direct estimates, we study their approximation behaviour and obtain quantitative estimates for the rate of convergence. The obtained results show that the modified operators provide improved approximation characteristics compared with the classical Szász–Mirakyan operators under suitable conditions. These findings contribute to the theory of positive linear operators and provide a useful framework for approximation processes on unbounded intervals.</p>