  We attempt to simultaneously explain the neutrino oscillation data and the
observed $(g-2)_{e,\mu}$ in a hidden gauge $U(1)_X$ model where all the
Standard Model(SM) fields are $U(1)_X$ singlets. The minimal version of this
model calls for four exotic scalars and two pairs of vector fermions, and all
are charged under $U(1)_X$. We carefully consider the experimental limits on
charge lepton flavor violation without assuming any flavor symmetry and explore
the viable model parameter space. The model can accommodate the neutrino
oscillation data for both the normal and the inverted mass ordering while
explaining the central value of $\triangle a_e$ by adopting the fine structure
constant determined by using either Cesium or Rubidium atoms. However, mainly
constrained by the current experimental bound on ${\cal B}(\tau\rightarrow \mu
\gamma)$, this model predicts $\triangle a_\mu <5.5(8.0)\times 10^{-10}$ for
the normal(inverted) neutrino ordering. Moreover, while the muon Yukawa
coupling is close to the SM one, we find the magnitude of the electron Yukawa
coupling could be one order of magnitude larger than the SM prediction. This
abnormal electron Yukawa could be probed in the future FCC-ee collider and
plays an essential role in testing flavor physics.
