  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.
