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The CoYSb (Y = Cr, Mo and W) compounds which are XYZ type half-Heusler alloys and also exist in the face centred cubic MgAgAs-type struc-ture conform to F ̄43m space group. In the present work, these compoundsare investigated in different atomic arrangements called, Type-I, Type-II andType-III phases, using Generalized Gradient Approximation (GGA) in the Density Functional Theory (DFT) implemented in QE (Quantum EspressoAb-Initio Simulation Package). The ferromagnetic state of these alloys is studied after investigating their stable structural phase. The calculated electronic band structure and the total electronic density of states indicated nearly half-metallic behaviour in CoMoSb with a possibility of being used in spintronic application, metallic in CoWSb and half-metallic in CoCrSb, with the minority spin band gap of 0.81 eV. Furthermore, the calculated mechanical properties predicted an anisotropic behaviour of these alloys in the stable phase. Finally, due to its high Debye temperature value, CoCrSb possesses a stronger covalent bond than CoMoSb and CoWSb, respectively.