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The non-thermal dark matter (DM) production via the so-called freeze-inmechanism provides a simple alternative to the standard thermal WIMP scenario.In this work, we consider a popular $U(1)_{B-L}$ extension of the standardmodel (SM) in the context of inverse seesaw mechanism which has at least one(fermionic) FIMP DM candidate. Due to the added $\mathbb{Z}_{2}$ symmetry, a SMgauge singlet fermion, with mass of order keV, is stable and can be a warm DMcandidate. Also, the same $\mathbb{Z}_{2}$ symmetry helps the lightestright-handed neutrino, with mass of order GeV, to be a stable or long-livedparticle by making a corresponding Yukawa coupling very small. This provides apossibility of a two component DM scenario as well. Firstly, in the absence ofa GeV DM component (i.e., without tuning its corresponding Yukawa coupling tobe very small), we consider only a keV DM as a single component DM, which isproduced by the freeze-in mechanism via the decay of the extra $Z'$ gauge bosonassociated to $U(1)_{B-L}$ and can consistently explain the DM relic densitymeasurements. In contrast with most of the existing literature, we have found areasonable DM production from the annihilation processes. After numericallystudying the DM production, we show the dependence of the DM relic density as afunction of its relevant free parameters. We use these results to obtain theparameter space regions that are compatible with the DM relic density bound.Secondly, we study a two component DM scenario and emphasize that the currentDM relic density bound can be satisfied for a wide range of parameter space.

FIMP dark matter candidate(s) in a $B-L$ model with inverse seesaw mechanism