  Exchanging a $Z^\prime$ gauge boson is a favored mechanism to solve the muon
$(g-2)_\mu$ anomaly. Among such models the $Z^\prime$ from $U(1)_{L_\mu -
L_\tau}$ gauge group has been extensively studied. In this model the same
interaction addressing $(g-2)_\mu$, leads to an enhanced muon neutrino trident
(MNT) process $\nu_\mu N \to \nu_\mu \mu \bar \mu N$ constraining the
$Z^\prime$ mass to be less than a few hundred MeV. Many other $Z^\prime$ models
face the same problem. It has long been realized that the coupling of
$Z^\prime$ in the model can admit $(\bar \mu \gamma^\mu \tau + \bar \nu_\mu
\gamma^\mu L \nu_\tau)Z^\prime_\mu$ interaction which does not contribute to
the MNT process. It can solve $(g-2)_\mu$ anomaly for a much wider $Z^\prime$
mass range. However this new interaction induces $\tau \to \mu \bar\nu_\mu
\nu_\tau$ which rules out it as a solution to $(g-2)_\mu$ anomaly. Here we
propose a mechanism by introducing type-II seesaw $SU(2)_L$ triplet scalars to
evade constraints from all known data to allow a wide $Z^\prime$ mass range to
solve the $(g-2)_\mu$ anomaly. This mechanism opens a new window for $Z^\prime$
physics.
