  We consider a $U(1)_X\otimes \mathbb{Z}_2\otimes \mathbb{Z}'_2$ extension of
the Standard Model (SM), where the $U(1)_X$ charge of an SM field is given by a
linear combination of its hypercharge and B$-$L number. Apart from the SM
particle content, the model contains three right-handed neutrinos (RHNs)
$N_R^i$ and two scalars $\Phi$, $\chi$, all singlets under the SM gauge group
but charged under $U(1)_X$ gauge group. Two of these additional fields, fermion
$N_R^3$ is odd under $\mathbb{Z}_2$ and scalar $\chi$ is odd under
$\mathbb{Z}'_2$ symmetry. Thus both $\chi$ and $N_R^3$ contribute to the
observed dark matter relic density, leading to two-component dark matter
candidates. We study in detail its dark matter properties such as relic density
and direct detection taking into account the constraints coming from collider
studies. We find that in our model, there can be possible annihilation of one
Dark Matter (DM) into the other, which may potentially alter the relic density
in a significant way.
