In this work, we discuss two component fermionic FIMP dark matter (DM) in a popular $B-L$ extension of the standard model (SM) with inverse seesaw mechanism. Due to the introduced $mathbb{Z}_{2}$ discrete symmetry, a keV SM gauge singlet fermion is stable and can be a warm DM candidate. Also, this $mathbb{Z}_{2}$ symmetry helps the lightest right-handed neutrino, with mass of order GeV, to be a long-lived or stable particle by choosing a corresponding Yukawa 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 a keV 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 correct ballpark DM relic density bound can be achieved for a wide parameter space.
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