  We propose a class of models providing an explanation of the origin of light
neutrino masses, the baryon asymmetry of the Universe via leptogenesis and
offering viable dark matter candidates. In these models the Majorana masses of
the active neutrino are generated by the inverse seesaw mechanism with the
lepton number violating right-handed Majorana neutrino masses $\mu$ arising at
three loops. The latter is ensured by the preserved discrete symmetries, which
also guarantee the stability of the dark matter candidate. We focus on one of
these models and perform a detailed analysis of the phenomenology of its
leptonic sector. The model can successfully accommodate baryogenesis through
leptogenesis in both weak and strong washout regimes. The lightest heavy
fermion turns out to be a viable dark matter candidate, provided that the
entries of the Majorana submatrix $\mu$ are in the keV to MeV range. The
solutions are consistent with the experimental constraints, accommodating both
mass orderings for active neutrinos, in particular charged-lepton flavor
violating decays $\mu\to e\gamma$, $\mu\to eee$, and the electron-muon
conversion processes get sizable rates within future sensitivity reach.
