  We study the phenomenology of a Standard Model (SM) extension with two
charged singlet scalars and three right handed (RH) neutrinos at an
electron-positron collider. In this model, the neutrino mass is generated
radiatively at three-loop, the lightest RH neutrino is a good dark matter
candidate; and the electroweak phase transition strongly first order as
required for baryogenesis. We focus on the process $e^{+}+e^{-}\rightarrow
e^{-}\mu^{+}+E_{miss}$, where the model contains new lepton flavor violating
interactions that contribute to the missing energy. We investigate the
feasibility of detecting this process at future $e^{-}e^{+}$ linear colliders
at different center of mass energies: $E_{CM}$=250, 350, 500 GeV and 1 TeV.
