Topological “Fermi-arc” states exist on certain surfaces of Weyl semimetals. They connect the surface projection of the bulk Weyl nodes. However, the actual connectivity among them remains ambiguous in the presence of multiple pairs of surface projected Weyl nodes. We use Fourier-transform scanning tunneling spectroscopy to verify the classification of the ferromagnetic Co₃Sn₂S₂ as a magnetic Weyl semimetal as well as its time reversal broken origin. By studying three different surface terminations we show that both the Fermi-arc connectivity as well as the Fermi-arc contour in Co₃Sn₂S₂ vary with the different surface potential. While on the Sn surface we find intra-Brillouin zone connectivity, on the Co surface the Fermi arcs connect Weyl nodes across the Brillouin zone edge. On the S termination the Fermi–arcs hybridize with non-topological bulk and thus their connectivity remain obscured.