To determine the structural, mechanical, electronic, magnetic, optical, and thermoelectric properties of novel quaternary Heusler alloys type ZrCoYAs (Y= Fe and Mn), we used DFT with WIEN2k. Our results showed that the ferromagnetic Y-type-III phase is more stable due to the higher negative values of their formation energy. We calculated and discussed the elastic constants Cij, which are used to calculate the mechanical properties. The Spin-polarized band structure and DOS calculations using the GGA-PBE and GGA + U approach display a metallic character. However, using the mBJ-GGA-PBE and mBJ-GGA + U approach show a half-metallic character, a semiconductor for the spin-down channel with a direct band gap of 0.61 eV with mBJ-GGA-PBE and 0.74 eV with mBJ-GGA + U for ZrCoMnAs and a direct band gap of 0.43 eV with mBJ-GGA-PBE and indirect band gap with 0.39 eV with mBJ-GGA + U for ZrCoFeAs, in contrast, the spin-up channel is metallic, with 100 % spin polarization and an integer magnetic moment of 1.00 μB for ZrCoMnAs and 2.00 μB for ZrCoFeAs, obeying the Slater-Pauling rule. The estimated Curie temperatures of ZrCoMnAs and ZrCoFeAs are 204 K using the new model, 421 K using MFA, and 385 K using the new model, 1627 K using MFA, respectively. As exchange-correlation potential, MBJ and MBJ + U provide a better description of the electronic and magnetic properties of ZrCoMnAs and ZrCoFeAs compounds. Important optical properties such as dielectric function, absorption coefficient, refractive index, optical conductivity, reflectivity, and electron energy loss function are calculated in the infrared, visible, and ultraviolet range. The static dielectric function suggests that ZrCoMnAs possesses greater polarizability. Both alloys exhibit similar behavior in the far ultraviolet region range and reach a maximum absorption in the ultraviolet range. The half-metallic character of both alloys is revealed from the reflectivity at zero frequency. The calculation of the thermoelectric properties shows positive Seebeck coefficients, indicating that these Heuslers are p-type. Furthermore, the highest power factor is observed at a temperature of 1400 K. The maximum value of ZT is ∼1.1 at 1400 K for ZrCoFeAs and ZrCoMnAs. These studies show that these alloys may have potential applications in the thermoelectric applications.