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In this paper we have studied neutrino masses and mixings by adding a scalartriplet $\eta$ to the particle content of minimal inverse seesaw. We haverealised this extension of minimal inverse seesaw by implementing an isomorphicmodular group $\Gamma(3)$ and a non-abelian discrete symmetry group $A_4$. Wehave also used $Z_3$ symmetry group to restrain certain interaction terms inthe lagrangian of the model. We have studied baryon asymmetry of the universe,neutrinoless double-beta decay and dark matter in our work. In order to checkthe consistency of our model with various experimental constraints, we havetherefore calculated effective mass, relic density and baryogenesis vialeptogenesis. Interestingly, we have found our model quite compatible with theexperimental bounds and is also successful in producing the neutrino masses andmixings in the 3$\sigma$ range.

Leptogenesis and dark matter in minimal inverse seesaw using $A_4$ modular symmetry