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Left Right Symmetric Model (LRSM) being an extension of the Standard model ofparticle physics incorporates within itself Type-I and Type-II seesaw massterms naturally. Both the mass terms can have significant amount ofcontribution to the resulting light neutrino mass within the model and hence onthe different phenomenology associated within. In this paper, we havethoroughly analyzed and discussed the implications of specifying differentweightages to the type-I and type-II mass terms and also the study has beencarried out for different values of $M_{W_R}$ which is mass of the right-handedgauge boson. This paper also gives a deeper insight into the new physicscontributions of Neutrinoless Double Beta Decay $(0\nu\beta\beta)$ and theirvariations with the net baryon asymmetry arising out of the model. Therefore,the main objective of the present paper rests on investigating the implicationsof imposing different weightage to the type-I and type-II seesaw terms anddifferent values of $M_{W_R}$ on the new physics contributions of$0\nu\beta\beta$ and net baryon asymmetry arising out as a result of resonantleptogenesis. LRSM in this work has been realized using modular group of level3, $\Gamma(3)$ which is isomorphic to non-abelian discrete symmetry group$A_4$, the advantage being the non-requirement of flavons within the model andhence maintaining the minimality of the model.

$M_{W_R}$ dependence of leptogenesis in Minimal Left-Right Symmetric Model with different strengths of Type-II seesaw mass