  The heavy singlet Majorana neutrinos are introduced to generate the neutrino
mass in the so-called phenomenological type-I seesaw mechanism. The phenomena
induced by the heavy Majorana neutrinos are important to search for new
physics. In this paper, we explore the heavy Majorana neutrino production and
decay at future $e^{-}p$ colliders. The corresponding cross sections via $W$
and photon fusion are predicted for different collider energies. Combined with
the results of the heavy Majorana neutrino production via single $W$ exchange,
this work can provide helpful information to search for heavy Majorana
neutrinos at future $e^{-}p$ colliders.

High Energy Physics - Phenomenology