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We construct a scotogenic Majorana neutrino mass model in a gauged $U(1)_X$extension of the standard model, where the mass of the gauge boson and theunbroken gauge symmetry, which leads to a stable dark matter (DM), can beachieved through the Stueckelberg mechanism. It is found that the simplestversion of the extended model consists of the two inert-Higgs doublets and onevector-like singlet fermion. In addition to the Majorana neutrino mass, westudy the lepton flavor violation (LFV) processes, such as $\ell_i \to \ell_j\gamma$, $\ell_i \to 3 \ell_j$, $\mu-e$ conversion rate in nucleus, andmuonium-antimuonium oscillation. We show that the sensitivities of $\mu\to 3e$and $\mu-e$ conversion rate designed in Mu3e and COMET/Mu2e experiments makeboth decays the most severe constraints on the $\mu\to e$ LFV processes. It isfound that $\tau\to \mu \gamma$ and $\tau\to 3\mu$ can reach the designedsignificance level of Belle II. In addition to explaining the DM relic density,we also show that the DM-nucleon scattering cross section can satisfy thecurrently experimental limit of DM direct detection.

Lepton flavor violation and scotogenic Majorana neutrino mass in a Stueckelberg $U(1)_X$ model