  We propose an extension of the Standard Model gauge symmetry by the gauge
group $U(1)_{T3R}$ in order to address the Yukawa coupling hierarchy between
the third generation fermions and the first two generation fermions of the SM.
We assume that only the right-handed fermions of the first two generations are
charged under the $U(1)_{T3R}$. In addition to the new dark gauge boson, we
have a dark scalar particle whose vacuum expectation value (vev) breaks the
$U(1)_{T3R}$ symmetry down to $Z_2$ symmetry and also explains the hierarchy
problem. A vev of $\cal O$(GeV) is required to explain the mass parameters of
the light flavor sector naturally. The dark matter (DM) particle arising from
the model naturally has mass in the $\mathcal {O}$(1-100) MeV range. The model
satisfies all the current constraints. We discuss the various prospects of the
direct detection of the dark matter. We get both elastic and inelastic spin
independent DM-nucleon scattering. The dark matter obtains the correct thermal
relic density by annihilation.
