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In this work, we discuss two component fermionic FIMP dark matter (DM) in apopular $B-L$ extension of the standard model (SM) with inverse seesawmechanism. Due to the introduced $\mathbb{Z}_{2}$ discrete symmetry, a keV SMgauge singlet fermion is stable and can be a warm DM candidate. Also, this$\mathbb{Z}_{2}$ symmetry helps the lightest right-handed neutrino, with massof order GeV, to be a long-lived or stable particle by choosing a correspondingYukawa coupling to be very small. Firstly, in the absence of a GeV DM component(i.e., without tuning its corresponding Yukawa coupling), we consider only akeV DM as a single component DM produced by the freeze-in mechanism. Secondly,we study a two component FIMP DM scenario and emphasize that the correctballpark DM relic density bound can be achieved for a wide parameter space.

Two component FIMP DM in a $U(1)_{B-L}$ extension of the SM