  The effect of a strongly magnetized cold plasma on the Compton-like
photoproduction of a neutrino-antineutrino pair on an electron, $\gamma e \to e
\nu \bar \nu$, has been considered. The contribution of this process to the
neutrino emissivity in both the non-resonance and the resonance cases has been
calculated with taking account of the photon dispersion properties in medium.
Our results show that the neutrino emissivity owing to the $\gamma e \to e \nu
\bar \nu$ reaction is significantly modified as compared to the previously
reported data.
