Ionization potentials, excitation energies, transition properties, and hyperfine structure constants of the low-lying $3p^6 3d^{9} ^2D_{5/2}$, $3p^6 3d^{9} ^2D_{3/2}$, $3p^5 3d^{10} ^2P_{3/2}$ and $3p^5 3d^{10} ^2P_{1/2}$ atomic states of the Co-like highly-charged ions such as Y$^{12+}$, Zr$^{13+}$, Nb$^{14+}$, Mo$^{15+}$, Tc$^{16+}$, Ru$^{17+}$, Rh$^{18+}$, Pd$^{19+}$, Ag$^{20+}$ and Cd$^{21+}$ are investigated. The singles and doubles approximated relativistic coupled-cluster theory in the framework of one electron removal Fock-space formalism is employed over the Dirac-Hartree-Fock calculations to account for the electron correlation effects for determining the aforementioned properties. Higher-order relativistic corrections due to the Breit interaction and quantum electrodynamics effects in the evaluation of energies are also quantified explicitly. Our estimated values are compared with the other available theoretical calculations and experimental results, which are found to be in good agreement with each other.