Motivated by the recently reported excess in electron recoil events by the XENON1T collaboration, we propose an inelastic fermion dark matter (DM) scenario within the framework of a gauged Lμ−Lτ extension of the standard model which can also accommodate tiny neutrino masses as well as anomalous muon magnetic moment (g−2)μ. A Dirac fermion DM, naturally stabilised due to its chosen gauge charge, is split into two pseudo-Dirac mass eigenstates due to Majorana mass term induced by singlet scalar which also takes part in generating right handed neutrino masses responsible for type I seesaw origin of light neutrino masses. The inelastic down scattering of heavier DM component can give rise to the XENON1T excess for keV scale mass splitting with lighter DM component. We fit our model with XENON1T data and also find the final parameter space by using bounds from (g−2)μ, DM relic, lifetime of heavier DM, inelastic DM-electron scattering rate, neutrino trident production rate as well as other flavour physics, astrophysical and cosmological observations. A tiny parameter space consistent with all these bounds and requirements will face further scrutiny in near future experiments operating at different frontiers. © 2020 The Authors