Reproducing the observed quenched fraction of satellite galaxies has been a long-standing issue for galaxy formation models. We modify the treatment of environmental effects in our state-of-the-art GAlaxy Evolution and Assembly (GAEA) semi-analytic model to improve our modelling of satellite galaxies. Specifically, we implement gradual stripping of hot gas, ram-pressure stripping of cold gas, and an updated algorithm to account for angular momentum exchanges between the gaseous and stellar disc components of model galaxies. Our updated model predicts quenched fractions that are in good agreement with local observational measurements for central and satellite galaxies, and their dependencies on stellar mass and halo mass. We also find consistency between model predictions and observational estimates of quenching times for satellite galaxies, H I, H-2 fractions of central galaxies, and deficiencies of H I, H-2, SFR of galaxies in cluster haloes. In the framework of our updated model, the dominant quenching mechanisms are hot gas stripping for low-mass satellite galaxies, and AGN feedback for massive satellite galaxies. The ram-pressure stripping of cold gas only affects the quenched fraction in massive haloes with M-h > 10(13.5) M-circle dot, but is needed to reproduce the observed H I deficiencies.