  We consider a class of gauged $U(1)$ extensions of the Standard Model (SM),
where the light neutrino masses are generated by an inverse seesaw mechanism.
In addition to the three right handed neutrinos, we add three singlet fermions
and demand an extra $Z_2$ symmetry under which, the third generations of both
of the neutral fermions are odd, which in turn gives us a stable dark matter
candidate. We express the $U(1)$ charges of all the fermions in terms of the
U(1) charges of the standard model Higgs and the new complex scalar. We study
the bounds on the parameters of the model from vacuum stability, perturbative
unitarity, dark matter relic density and direct detection constraints. We also
obtain the collider constraints on the $Z'$ mass and the $U(1)'$ gauge
coupling. Finally we compare all the bounds on the $Z'$ mass versus the $U(1)'$
gauge coupling plane.
