  We suggest a new family of Co/Ni-based materials that may host unconventional
high temperature superconductivity (high-T$_c$). These materials carry layered
square lattices with each layer being formed by vertex-shared transition metal
tetrahedra cation-anion complexes. The electronic physics in these materials is
determined by the two dimensional layer and is fully attributed to the three
near degenerated $t_{2g}$ d-orbitals close to a $d^7$ filling configuration in
the d-shell of Co/Ni atoms . The electronic structure meets the necessary
criteria for unconventional high T$_c$ materials proposed recently by us to
unify the two known high-T$_c$ families, cuprates and iron-based
superconductors. We predict that they host superconducting states with a d-wave
pairing symmetry with T$_c$ potentially higher than those of iron-based
superconductors. These materials, if realized, can be a fertile new ground to
study strongly correlated electronic physics and provide decisive evidence for
superconducting pairing mechanism.
