$0\nu\beta\beta$ in left-right theories with Higgs doublets and gauge coupling unification

We consider a version of Left-Right Symmetric Model with Higgs bidoublet ($\Phi$) ($B-L=0$), Higgs doublets ($H_{L,R}$) ($B-L=1$) and a charged scalar ($\delta^+$) ($B-L=2$) leading to radiatively generated Majorana masses for neutrinos and thereby, leads to new physics contributions to $0\nu\beta\beta$. We have embedded the model in a non-SUSY $SO(10)$ GUT leading to successful gauge coupling unification. The model can also be extended to phenomenologically detect $W_R, Z_R$ bosons in LHC and future collider searches. In the context of neutrinoless double beta decay, this model can saturate the present bound from GERDA and KamLAND-Zen experiments. Also, we briefly explain how keV-MeV range RH neutrino arising from our model can saturate various astrophysical and cosmological constraints and can be considered as warm Dark Matter (DM) candidate to address various cosmological issues.