We show how, in the $B-L$ extension of the SM (BLSM) with an Inverse Seesaw (IS) mechanism for neutrino mass generation, a light $Z^{\prime }$ state with moderate couplings to SM objects, hence ‘dark’ in its nature, can be associated, in conjunction with light sterile neutrinos, to some present day data anomalies, such as the anomalous magnetic moment of the muon as well as a possible signal indicating the existence of sterile neutrinos in neutrino beam experiments.