Two-component scalar and fermionic dark matter candidates in a generic U$(1)_X$ model

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.