MnCoGe alloy is a promising candidate for room-temperature magnetic refrigeration applications, and the magnetocaloric effect in this family has a close relationship with the nature of phase transition. In this work, we presented a systematic study focusing on the phase transition, magnetic entropy change, and magnetic interaction in four compositions. The Banerjee criterion, Landau theory, and universal behavior were performed to distinguish the characteristic of second-order transition. It is found that the theoretical magnetic entropy changes based on Landau theory are in good agreement with the experimental findings, indicating the reliability of this method to evaluate magnetocaloric property. Moreover, the fitting parameters determined from the rescaled magnetic entropy change curves and field dependence of magnetic entropy change are used to give a better understanding of phase transition and magnetic refrigerant performance. Reliable critical exponents from three techniques suggest long-range magnetic couplings in this system. Additionally, the differences in critical behavior with Ag substitution are described by calculation of density of the effective exponents ((eff) and (eff)) and exchange distance J(r). The very stable nature of phase transition and abundant availability make this system suitable for thermomagnetic power generation applications.