  We consider a general, anomaly free U$(1)^\prime$ extension of the Standard
Model (SM) where the neutrino mass is generated at the tree level via the
inverse seesaw mechanism. The model contains three right handed neutrinos,
three additional singlet fermions, one extra complex scalar and a neutral gauge
boson $(Z^\prime)$. Instead of resorting to a specific $U(1)$ extension, we
consider a class of models by taking the $U(1)^\prime$ charges of the scalars
to be free parameters. Here, we assign one pair of the pseudo-Dirac degenerate
sterile neutrinos as Dark Matter (DM) candidates which are produced by the
freeze-in mechanism. Considering different mass regimes of the DM, $Z^\prime$
and reheating temperature, we obtain constraints on the $U(1)^\prime$ charges
giving the correct relic abundance. We have also obtained constraints on
$Z^\prime$ mass and coupling from consideration of relic density as well as
high energy collider experiments like ATLAS in case of heavy $Z^\prime$ or in
intensity and lifetime frontier experiments like DUNE, FASERs, and ILC beam
dump which are looking for light $Z^\prime$. Additionally, in this model, the
decay of pseudo-Dirac DM into active neutrinos can explain the 511 keV line
observed by the INTEGRAL satellite.
