We study a model of neutrino and dark matter within the framework of a minimal extended seesaw. This framework is based on $A_4$ flavor symmetry along with the discrete $Z_4$ symmetry to stabilize the dark matter and construct desired mass matrices for neutrino mass. We use a non-trivial Dirac mass matrix with broken $mu - tau$ symmetry to generate the leptonic mixing. A non-degenerate mass structure for right-handed neutrinos is considered to verify the observed baryon asymmetry of the Universe via the mechanism of thermal Leptogenesis. The scalar sector is also studied in great detail for a multi-Higgs doublet scenario, considering the lightest $Z_4$-odd as a viable dark matter candidate. A significant impact on the region of DM parameter space, as well as in the fermionic sector, are found in the presence of extra scalar particles.
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