We predict Co-based chalcogenides with a diamond-like structure can host unconventional high temperature superconductivity (high-$T_c$). The essential electronic physics in these materials stems from the Co layers with each layer being formed by vertex-shared CoA$_4$ (A=S,Se,Te) tetrahedra complexes, a material genome proposed recently by us to host potential unconventional high-$T_c$ close to a $d^7$ filling configuration in 3d transition metal compounds. We calculate the magnetic ground states of different transition metal compounds with this structure. It is found that (Mn,Fe,Co)-based compounds all have a G-type antiferromagnetic(AFM) insulating ground state while Ni-based compounds are paramagnetic metal. The AFM interaction is the largest in the Co-based compounds as the three $t_{2g}$ orbitals all strongly participate in AFM superexchange interactions. The abrupt quenching of the magnetism from the Co to Ni-based compounds is very similar to those from Fe to Co-based pnictides in which a C-type AFM state appears in the Fe-based ones but vanishes in the Co-based ones. This behavior can be considered as an electronic signature of the high-$T_c$ gene. Upon doping, as we predicted before, this family of Co-based compounds favor a strong d-wave pairing superconducting state.
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