  We explain the existence of neutrino masses and their flavor structure, dark
matter relic abundance and the observed 3.5 keV X-ray line within the framework
of a gauged $U(1)_{L_{\mu} - L_{\tau}}$ extension of the "scotogenic" model. In
the $U(1)_{L_{\mu} - L_{\tau}}$ symmetric limit, two of the the RH neutrinos
are degenerate in mass, while the third is heavier. The $U(1)_{L_{\mu} -
L_{\tau}}$ symmetry is broken spontaneously. Firstly, this breaks the
$\mu-\tau$ symmetry in the light neutrino sector. Secondly, this results in
mild splitting of the two degenerate RH neutrinos, with their mass difference
given in terms of the $U(1)_{L_{\mu} - L_{\tau}}$ breaking parameter. Finally,
we get a massive $Z_{\mu\tau}$ gauge boson. Due to the added $Z_2$ symmetry
under which the RH neutrinos and the inert doublet are odd, the canonical
Type-I seesaw is forbidden and the tiny neutrino masses are generated
radiatively at one loop. The same $Z_2$ symmetry also ensures that the lightest
RH neutrino is stable and the other two can only decay into the lightest one.
This makes the two nearly-degenerate lighter neutrinos a two-component dark
matter, which in our model are produced by the freeze-in mechanism via the
decay of the $Z_{\mu\tau}$ gauge boson in the early universe. We show that the
next-to-lightest RH neutrino has a very long lifetime and decays into the
lightest one at the present epoch explaining the observed 3.5 keV line.
