In this paper, we introduce a new family of Baskakov-Kantorovich operators that depend on a function ψ. We compare these new ψ-Baskakov-Kantorovich operators with the classical Baskakov-Kantorovich operators to evaluate their approximation results. Our analysis shows that these new operators provide better approximation results across the entire interval [0 ,∞). We demonstrate their uniform convergence in weighted spaces and determine their convergence rates using both first and second-order moduli of continuity. We also prove that these operators preserve shape preserving properties. We support our findings with graphical and numerical examples.