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We propose an anomaly free unified scenario by invocation of an extra local${\rm U(1)}_{L_{\mu}-L_{\tau}}$ gauge symmetry. This scenario simultaneouslyresolves the $R_{K^{(*)}}$ anomalies, the dark matter puzzle and thelong-standing discrepancy in muon's anomalous magnetic moment. A complex scalar($\eta$) having nonzero ${L_{\mu}-L_{\tau}}$ charge has been introduced tobreak this new U(1) symmetry spontaneously. Moreover, for the purpose ofstudying dark matter phenomenology and $R_{K^{(*)}}$ anomalies in a correlatedmanner, we introduce an inert ${\rm SU(2)}_L$ scalar doublet ($\Phi$), a$\mathbb{Z}_2$-odd real singlet scalar ($S$) and a $\mathbb{Z}_2$-odd colouredfermion ($\chi$) which transforms vectorially under the ${\rmU(1)}_{L_{\mu}-L_{\tau}}$ symmetry. This extra gauge symmetry provides a newgauge boson $Z_{\mu\tau}$ which not only gives additional contribution to both$b\to s \ell\ell$ transition and $(g-2)_{\mu}$ but also provides a crucialannihilation channel for dark matter candidate $\rho_1$ of the presentscenario. This $\rho_1$ is an admixture of CP-even neutral component of $\Phi$and $S$. Our analysis shows that the low mass dark matter regime($M_{\rho_1}\lesssim 60$ GeV) is still allowed by the experiments like XENON1T,LHC (via Higgs invisible branching) and Fermi-LAT, making the dark matterphenomenology drastically different from the standard Inert Doublet and theScalar Singlet models. Furthermore, the present model is also fairly consistentwith the observed branching ratio of $B\to X_s\gamma$ in $3\sigma$ range and isquite capable of explaining neutrino masses and mixings via Type-I seesawmechanism if we add three right handed neutrinos in the particle spectrum.Finally, we use the latest ATLAS data of non-observation of a resonant$\ell^+\ell^-$ signal at the 13 TeV LHC to constrain the mass-coupling plane of$Z_{\mu\tau}$.

Reconciling dark matter, $R_{K^{(*)}}$ anomalies and $(g-2)_{\mu}$ in an ${L_{\mu}-L_{\tau}}$ scenario