Very recently, the half-metallic compound Co$_3$Sn$_2$S$_2$ was predicted to be a magnetic WSM with Weyl points only 60 meV above the Fermi level ($E_F$). Owing to the low charge carrier density and large Berry curvature induced, Co$_3$Sn$_2$S$_2$ possesses both a large anomalous Hall conductivity (AHC) and a large anomalous Hall angle (AHA), which provide strong evidence for the existence of Weyl points in Co$_3$Sn$_2$S$_2$. In this work, we theoretically studied the surface topological feature of Co$_3$Sn$_2$S$_2$ and its counterpart Co$_3$Sn$_2$Se$_2$. By cleaving the sample at the weak Sn-S/Se bonds, one can achieve two different surfaces terminated with Sn and S/Se atoms, respectively. The resulting Fermi arc related states can range from the energy of the Weyl points to $E_F$-0.1 eV in the Sn-terminated surface. Therefore, it should be possible to observe the Fermi arcs in angle-resolved photoemission spectroscopy (ARPES) measurements. Furthermore, in order to simulate quasiparticle interference (QPI) in scanning tunneling microscopy (STM) measurements, we also calculated the joint density of states (JDOS), which revealed that the QPI patterns arising from Fermi arc related scatterings are clearly visible for both terminals. This work would be helpful for a comprehensive understanding of the topological properties of these two magnetic WSMs and further ARPES and STM measurements.
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