  We analyze the implications of an extended 2HDM theory in quark masses and
mixings, electroweak precision tests, charged lepton flavor violating (CLFV)
decays, neutrino trident production, B meson, $g-2$ muon and W anomalies. In
the extended 2HDM theory considered in this work, the SM gauge symmetry is
enlarged by the local $U(1)^{\prime}$ symmetry, whereas its scalar and fermion
sectors are augmented by the inclusion of a gauge singlet scalar and vectorlike
fermions, respectively. Within the framework of this model, we determine the
allowed ranges of the $Z^{\prime}$ gauge boson mass consistent with the
constraints arising from neutrino trident production, $R_{K^{*}}$ anomaly,
$B_{s}$ meson oscillation. We conclude the $R_{K^{*}}$ and muon $g-2$ anomalies
cannot be simultaneously explained by the same new physics under all the
constraints. Besides that, we found that the new physics sources, the
$Z^{\prime}$ and non SM scalars cannot be connected via the scalar potential.
Furthermore, we have found that the model under consideration can successfully
comply with the constraints arising from oblique $T,S,U$ parameters as well as
with the $W$ mass and $g-2$ muon anomalies. In particular we found that the
muon $g-2$ anomaly, whose dominant contribution arises from the one loop level
scalar exchange, can be successfully accommodated within the $2\sigma$
experimentally allowed range.

High Energy Physics - Phenomenology