We suggest that Cobalt-Oxychalcogenide layers constructed by vertex sharing CoA2O2 (A=S,Se,Te) tetrahedra, such as BaCoAO, are strongly correlated multi-orbital electron systems that can provide important clues on the cause of unconventional superconductivity. Differing from cuprates and iron-based superconductors, these systems lack of the C4 rotational symmetry. However, their parental compounds possess antiferromagnetic(AFM) Mott insulating states through pure superexchange interactions and the low energy physics near Fermi surfaces upon doping is also attributed mainly to the three t2g orbitals that dominate the AFM interactions. We derive a low energy effective model for these systems and predict that a d-wave-like superconducting state with reasonable high transition temperature can emerge by suppressing the AFM ordering even if the pairing symmetry can not be classified by the rotational symmetry any more.In the past three decades, two families of unconventional high temperature superconductors (high -T c ), cuprates[1] and iron-based superconductors[2], were discovered. Enormous research efforts have been devoted to understand their origin of high T c . However, lacking of general principles that can guide us to search for new high T c materials is still the major barrier in reaching a consensus in this field.Recently, we have shown that the two known families of high-T c share a common electronic property-those dorbitals that make the strongest in-plane d-p couplings are isolated near Fermi surface energy [3][4][5]. This special electronic character separates the two families of high T c materials from other correlated electronic materials. We have further argued that this character can only be realized in very limited special cases so that it can serve as the clue to guide us in searching for next families of unconventional high T c materials. Following this guide, we have found that the condition can be realized in two special electronic structures. The first one is a two dimensional hexagonal lattice formed by edge-shared trigonal biprymidal complexes [3] and the second one is a two dimensional square lattice formed by vertex-shared tetrahedra complexes [6]. In both cases, the condition is satisfied when the electron filling configuration in cation atoms is near d 7 , which suggests that layered Co 2+ /Ni 3+ based materials can be promising high T c families. Furthermore, following the Hu-Ding principle [7] of the pairing symmetry selection, the d + id and d pairing symmetries are selected respectively in these two families.Confirming the above predictions can promisingly settle the elusive unconventional high T c mechanism and open the window for theoretically designing high T c materials. However, materials with above characteristics are new materials and it is unknown whether they can be synthesized successfully.In this paper, we turn our attention to a family of ma-