  We investigate the low energy properties of an effective local model with
flipped $SU(5)\times U(1)_{\chi}$ gauge group, constructed within the framework
of F-theory. Its origin is traced back to the $SO(10)$ symmetry -- associated
with a geometric singularity of the compactification manifold -- broken by an
internal flux which is turned on along the seven-brane in the $U(1)_{\chi}$
direction. Topological properties and the choice of flux parameters determine
the massless spectrum of the model to be that of the minimal flipped $SU(5)$
supplemented with an extra right-handed electron-type state and its complex
conjugate, $E^c+\bar E^c$, as well as neutral singlet fields. The subsequent
symmetry breaking to the $SU(3)\times SU(2)\times U(1)_Y$ gauge group occurs
with a Higgs pair in $10+\overline{10}$ representations of $SU(5)$. Next we
proceed to the phenomenological analysis of the resulting effective model and
the salient outcomes are: The $E^c+\bar E^c$ pair acquires a mass of few TeV
and as such could solve the $g_{\mu}-2$ discrepancy. Neutrino couplings to
extra neutral singlets lead to an inverse seesaw mechanism where an extra light
state could be a suitable dark matter candidate. The predictions of the model
for the ${0\nu}\beta\beta$ decay rate could be tested in near future
experiments. There are non-unitarity deviations from lepton mixing matrix
($U_{PMNS}$), which could in principle explain the new precision measurement of
the W-boson mass recently reported by CDF II collaboration.
