An inclusive investigation of electronic and magnetic properties of ordered and disordered (Ni,Co)MnGa quaternary Heusler alloy has been undertaken using the density functional theory-based full potential linearized augmented plane wave method within generalized gradient approximation as exchange-correlation potentials. We observe that the increasing Mn concentration in Ni1-xCoMn1+xGa (x = 0, 0.25, 0.50 and 0.75) lowers the ferromagnetic (FM) character of the parent (Ni,Co)MnGa alloy. This change creates two inequivalent Mn sites aligning antiparallel to each other and generates the ferrimagnetic (FiM) ordering in all resultant disordered alloys. Further, this replacement sets off a structural change from Y- to X-a-structure. The highest magnetic moment has been found to be 4.95 mu B for ordered (Ni,Co)MnGa alloy, whereas it decreases with increase in Mn-concentration for disordered systems. The variation of half-metallicity with increasing Mn concentration is analysed. The stability of FM and FiM state for the present ordered and disordered alloys, respectively, is also examined.