We have calculated the fundamental properties of CoHfSi and CoHfGe half-Heusler alloys within the density functional theory simulation scheme as embedded in Wien2k. First and foremost, the structural optimization signifies that both the alloys suitably crystallize in cubic C1b structure with Y1 as a dominant ferromagnetic phase. The electronic properties have been computed within the applied approximation schemes like Generalized Gradient Approximation and modified Becke-Johnson potential. The electronic properties of these half-Heusler exhibit a half-metallic character, which is additionally substantiated by the presence of an integer value of the magnetic moment. Further, the investigation of different thermodynamic parameters by utilization of the quasi-harmonic Debye model to examine the thermodynamic stability of alloys at various temperatures and pressure (0K to 900K and 0 GPa to 20 GPa). The Seebeck coefficients, electrical conductivity, thermal conductivity and power factor are scrutinized to comprehend the thermoelectric properties. The collected results indicate that these alloys are applicable for spintronic and thermoelectric.