Phenomenology of one zero texture Yukawa matrix in a flavor symmetric scotogenic model

The scotogenic model is well known for accommodating small neutrino mass and dark matter. Here, we have realized the scotogenic model with the help of discrete flavor symmetry $A_4\otimes Z_4$. We have obtained three one zero textures of Yukawa coupling matrices from the model and have studied its impact on neutrino phenomenology and related aspects of cosmology. On the basis of $\mu -\tau$ symmetry, we have further discarded two structures of one zero texture Yukawa coupling matrix. We further analyze if the effective mass of active neutrinos obtained by the virtue of the Yukawa coupling matrix is consistent with the KamLAND-Zen limit for 0$\nu \beta \beta$. Also different lepton flavor violating(LFV) processes such as $l_{\alpha}\longrightarrow l_{\beta}\gamma$and$l_{\alpha}\longrightarrow 3l_{\beta}$ are implemented and their influence on neutrino phenomenology is studied corresponding to the Yukawa coupling matrix. The entire work is carried out considering the dark matter mass($M_{DM}$) in the region $450-750$ GeV. We have also obtained some significant results for baryon asymmetry of the Universe in agreement with the one zero textures of the coupling matrices. Furthermore, interesting results for relic abundance on the basis of distinct mass splittings between the inert scalars.