abstract: The observed quenching fraction of satellite galaxies has long been, and to large extent still is, a serious issue for theoretical models of galaxy formation and evolution. The dominant quenching mechanism of satellites is still under debate. We present an updated version of the semi-analytic model GAEA that successfully reproduces the quenching fractions for both central and satellite galaxies, as well as HI and H2 fractions for central galaxies. Our model provides the best match compared to many state-of-art theoretical models. The model is implemented with gradual stripping of hot gas, ram-pressure stripping of cold gas, and an updated algorithm to account for angular momentum exchanges between gas and stellar disc. The model is in good agreement on HI, H2 and SFR deficiencies with observational measurements for satellites in cluster haloes. We find that the quenching fraction is mainly affected by modeling of hot-gas stripping, and the HI fraction is affected mainly by modeling of stripping of cold gas. The quenching mechanism depends on galaxy stellar mass. Low-mass galaxies are quenched by the combined effects of internal and external processes. The hot-gas stripping suppresses cooling, and the star formation related processes consume most of the baryons. Massive satellites are quenched because cooling is suppressed by AGN radio-mode feedback, leaving large amounts of baryons in hot gas to be stripped off.