We investigate constraints on the new B − L gauge boson (Z BL) mass and coupling (g BL) in a Uð1Þ B−L extension of the standard model (SM) with an SM singlet Dirac fermion (ζ) as dark matter (DM). The DM particle ζ has an arbitrary B − L charge Q chosen to guarantee its stability. We focus on the small Z BL mass and small g BL regions of the model, and find new constraints for the cases where the DM relic abundance arises from thermal freeze-out as well as freeze-in mechanisms. In the thermal freeze-out case, the dark matter coupling is given by g ζ ≡ g BL Q ≃ 0.016 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi m ζ ½GeV p to reproduce the observed DM relic density and g BL ≥ 2.7 × 10 −8 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi m ζ ½GeV p for the DM particle to be in thermal equilibrium prior to freeze-out. Combined with the direct dark matter detection constraints and the indirect constraints from cosmic microwave background and AMS-02 measurements, discussed in earlier papers, we find that the allowed mass regions are limited to be m ζ ≳ 200 GeV and M Z BL ≳ 10 GeV. We then discuss the lower g BL values where the freeze-in scenario operates and find the following relic density constraints on parameters depending on the g BL range and dark matter mass: Case (A): for g BL ≥ 2.7 × 10 −8 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi m ζ ½GeV p , one has g 2 ζ g 2 BL þ 0.82 1.2 g 4 ζ ≃ 8.2 × 10 −24 ; and Case (B): for g BL < 2.7 × 10 −8 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi m ζ ½GeV p , there are two separate constraints depending on m ζ. Case (B1): for m ζ ≲ 2.5 TeV, we find g 2 ζ g 2 BL ≃ 8.2 × 10 −24 ð m ζ 2.5 TeV Þ; and Case (B2): for m ζ ≳ 2.5 TeV, we have g 2 ζ g 2 BL ≃ 8.2 × 10 −24. For this case, we display the various parameter regions of the model that can be probed by a variety of "Lifetime Frontier" experiments such as FASER, FASER2, Belle II, SHiP, and LDMX.