  Since its inception, no decisive departure from the predictions of Standard
Model (SM) has been reported. But recently various experiments have observed
few hints of possible departure from SM predictions in lepton flavor
universality observables such as $R_{K^{(*)}}$, $P_{5}^{'}$, muon (g-2),
$R(D^{(*)})$ etc. Many of these observable where deviation from SM in the range
of (2-4)$\sigma$ were observed are related to muon ($\mu$) lepton. So these
deviations may be some hint of a possible New Physics (NP) in the muon sector.
In this work we extend the SM by introducing two SM singlet heavy charged
leptons ($F_{e},\ F_{\mu}$) whose left handed components are charged under a
new $U(1)_{F}$ gauge symmetry, one color triplet lepto-quark ($\phi_{Q}$)
doublet under $SU(2)_{L}$, one inert Higgs doublet ($\phi_{l}$), three very
heavy Majorana neutrinos ($N_{iR}$), all of which are odd under a $Z_{2}$
discrete symmetry. One more scalar ($\phi$) charged only under the $U(1)_{F}$
whose VEV give masses to the $U(1)_{F}$ gauge boson as well as the heavy
leptons. With these new particles, we show that the observed anomalies in the
muon sector as well as small neutrino masses can be explained with taking into
account all the other experimental and theoretical constrains till date.
