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Discrete symmetries being preferred to explain the neutrino phenomenology, we chose the simplest S 3 group and explore the implication of its modular form on neutrino masses and mixing.Non-trivial transformations of Yukawa couplings under this symmetry, make the model phenomenologically interesting by reducing the requirement of multiple scalar fields. This symmetry imposes a specific flavor structure to the neutrino mass matrix within the framework of less frequented type III seesaw mechanism and helps to explore the neutrino mixing consistent with the current observation. Apart, we also explain the preferred scenario of leptogenesis to explain the baryon asymmetry of the universe by generating the lepton asymmetry from the decay of heavy fermion triplet at TeV scale.

Modular symmetries have been impeccable in neutrino and quark sectors. This motivated us, to propose a variant of scotogenic model based on modular $A_4$ symmetry and realize the neutrino mass generation at one-loop level through radiative mechanism. Alongside, we discuss the lepton flavour violating processes $\mu \to e \gamma$, $\mu \to3e$ and $\mu - e $ conversion in the nucleus. The lightest Dirac fermion turns out to be potential dark matter candidate, made stable by suitable assignment of modular weights. The relic density of the same has been computed with annihilations mediated by inert scalars and new $U(1)$ gauge boson. The LEP-II and ATLAS dilepton constraints on the new gauge parameters are suitably considered to show the consistent parameter region.