  We propose a new neutrino flavor model based on a $D_{4}\times U(1)$ flavor
symmetry providing predictions for neutrino masses and mixing along with a
successful generation of the observed Baryon Asymmetry of the Universe (BAU).
After the spontaneous breaking of the flavor symmetry, the type I seesaw
mechanism leads to a light neutrino mass matrix with broken $\mu-\tau $
symmetry. By performing a numerical analysis, we find that the model favors a
normal mass hierarchy with the lightest neutrino mass lies in the range
$m_{1}\in \lbrack 2.516,21.351]$ m$\mathrm{eV}$. The phenomenological
implications of the neutrino sector are explored in detail and the results are
discussed. Moreover, the generation of BAU is addressed via the leptogenesis
mechanism from the decay of three right-handed neutrinos $N_{i}$. Through
analytical and numerical analysis of the baryon asymmetry parameter $Y_{B}$, a
successful unflavored leptogenesis takes place within the allowed parameter
space obtained from neutrino phenomenology. We also examine interesting
correlations between $Y_{B}$ and low energy observables and provide a
comprehensive discussion of the results.
