  A gauged U$(1)$ extension of the Standard Model (SM) is a simple and anomaly
free framework where three generations of Majorana type right-handed neutrinos
(RHNs) are introduced to generate light neutrino mass and flavor mixings
through the seesaw mechanism. We investigate such models at different hadron
and lepton colliders via $Z^\prime$ induced Majorana type RHNs pair production.
We derive bounds on U$(1)$ gauge coupling $(g^\prime)$ comparing the model
cross sections with experimentally observed data for different $Z^\prime$ mass
$(M_{Z^\prime})$ and RHNs mass $(M_N)$. Using these limits we estimate the
allowed RHN pair production cross section which can be manifested by lepton
number violating signatures in association with fat-jets at the hadron
colliders depending on the mass of the RHNs. Hence we study dilepton and
trilepton modes with fat-jet/s of the signal for different benchmark values of
$M_{Z^\prime}$ and $M_N$. Using fat-jet signatures and studying the signal and
corresponding SM backgrounds, we estimate bounds on $M_N-M_{Z^\prime}$ plane at
different center of mass energies which could be probed at different hadron
colliders. In the context of the lepton colliders we consider electron positron
initial states where Majorana type RHNs can be produced from $Z^\prime$
manifesting same sign dilepton plus jets signature and trilepton plus jets in
association with missing energy. Studying the signal and corresponding SM
backgrounds we estimate the bounds on the $M_N-M_{Z^\prime}$ plane for
different center of mass energies. In the context of U$(1)$ extension of the SM
there is an SM singlet BSM scalar which couples with the RHNs. We can probe the
Majorana nature of RHNs via this BSM scalar production at electron positron
colliders.
