Gauged U(1)Lμ−Lτ model has been advocated for a long time in light of muon g−2 anomaly, which is a more than 3σ discrepancy between the experimental measurement and the standard model prediction. We augment this model with three right-handed neutrinos (Ne,Nμ,Nτ) and a vector-like singlet fermion (χ) to explain simultaneously the non-zero neutrino masses and dark matter content of the Universe, while satisfying the anomalous muon g−2 constraints. We find that the model suffers stringent constraints from the simultaneous explanation of neutrino trident production and muon g−2 anomaly. In a large region of the parameter space, where contribution to muon g−2 anomaly comes partially and yet not ruled out by neutrino trident production, the model can explain the positron excess, observed at PAMELA, Fermi-LAT and AMS-02 through dark matter annihilation, while satisfying the relic density and direct detection limits. © 2017 The Authors