This paper explores the Kerr-MOG-(A)dS black hole solutions in scalar-tensor-vector (STVG) gravity, a theory that addresses galaxy rotation curves and galaxy clusters without invoking dark matter. The authors construct rotating black hole solutions with a cosmological constant, modifying the gravitational constant to $G = G_N(1 + \alpha)$. They investigate the effects of the MOG parameter and the cosmological constant on black hole shadows, finding that the apparent size of the shadow decreases as the cosmological constant increases, while the shadow expands with the MOG parameter, becoming more rounded. Numerical ray-tracing techniques are used to distinguish degeneracies between different black hole parameters, demonstrating that gravitational lensing and frame-dragging effectively resolve these degeneracies. The study contributes to a deeper understanding of black holes in modified gravity theories and their observational signatures.This paper explores the Kerr-MOG-(A)dS black hole solutions in scalar-tensor-vector (STVG) gravity, a theory that addresses galaxy rotation curves and galaxy clusters without invoking dark matter. The authors construct rotating black hole solutions with a cosmological constant, modifying the gravitational constant to $G = G_N(1 + \alpha)$. They investigate the effects of the MOG parameter and the cosmological constant on black hole shadows, finding that the apparent size of the shadow decreases as the cosmological constant increases, while the shadow expands with the MOG parameter, becoming more rounded. Numerical ray-tracing techniques are used to distinguish degeneracies between different black hole parameters, demonstrating that gravitational lensing and frame-dragging effectively resolve these degeneracies. The study contributes to a deeper understanding of black holes in modified gravity theories and their observational signatures.