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In this work, we studied baryogenesis via leptogenesis, neutrinoless doublebeta decay (NDBD) in the framework of LRSM where type I and type II seesawterms arises naturally. The type I seesaw mass term is considered to befavouring $\mu-\tau$ symmetry, taking into account the widely studiedrealizations of $\mu-\tau$ symmetric neutrino mass models, viz. TribimaximalMixing (TBM), Hexagonal Mixing (HM) and Golden Ratio Mixing (GRM) respectively.The required correction to generate a non vanishing reactor mixing angle$\theta_{13}$ is obtained from the perturbation matrix, type II seesaw massterm in our case. We studied the new physics contributions to NDBD andbaryogenesis ignoring the left-right gauge boson mixing and the heavy-lightneutrino mixing, keeping mass of the gauge bosons and scalars to be around TeVand studied the effects of the new physics contributions on the effective mass,NDBD half life and cosmological BAU and compared with the values imposed byexperiments. We basically tried to find the leading order contributions to NDBDand BAU, coming from type I or type II seesaw in our work.

Perturbations to $\mu-\tau$ symmetry, lepton Number Violation and baryogenesis in left-right symmetric Model