Production of heavy Majorana neutrino $N_{e}$ predicted by left-right symmetric extension of the Standard Model at future { ormalsize TeV} scale $ep$ colliders have been considered. In order to estimate potential of $ep$ colliders for $N_{e}$ search
we consider back-groundless process $e^{-}prightarrow e^{+}X$ which is consequence of Majorana nature of $N_{e}$. It is shown that { ormalsize linac-LHC} and { ormalsize linac-FCC} based $ep$ colliders will cover much wider regions of $N_{e}$ and $W_{R}$ masses than corresponding linear electron-positron colliders.
