  We propose an extension to the Standard Model accommodating two families of
Dirac neutral fermions and Majorana fermions under additional ${U(1)_{e-\mu}
\times Z_3\times Z_2}$ symmetries where ${U(1)_{e-\mu}}$ is a flavor dependent
gauge symmetry related to the first and second family of the lepton sector,
which features a two-loop induced neutrino mass model. The two families are
favored by minimally reproducing the current neutrino oscillation data and two
mass difference squares and canceling the gauge anomalies at the same time. As
a result, we have a prediction for neutrino masses. The lightest Dirac neutral
fermion is a dark matter candidate with tree-level interaction restricted to
electron, muon and neutrinos, which makes it difficult to detect in direct dark
matter search as well as indirect search focusing on the ${\tau}$-channel, such
as through ${\gamma}$-rays. It may however be probed by search for dark matter
signatures in electron and positron cosmic rays, and allows interpretation of a
structure appearing in the CALET electron+positron spectrum around 350-400 GeV
as its signature, with a boost factor $\approx$40 Breit-Wigner enhancement of
the annihilation cross section.
