Motivated by the growing evidence for lepton flavour universality violation after the first results from Fermilabs muon $(g-2)$ measurement, we revisit one of the most widely studied anomaly free extensions of the standard model namely, gauged $L_{mu}-L_{tau}$ model, known to be providing a natural explanation for muon $(g-2)$. We also incorporate the presence of dark matter (DM) in this model in order to explain the recently reported electron recoil excess by the XENON1T collaboration. We show that the same neutral gauge boson responsible for generating the required muon $(g-2)$ can also mediate interactions between electron and dark fermions boosted by dark matter annihilation. The required DM annihilation rate into dark fermion require a hybrid setup of thermal and non-thermal mechanisms to generate DM relic density. The tightly constrained parameter space from all requirements remain sensitive to ongoing and near future experiments, keeping the scenario very predictive.
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