In our recent paper (Das et al. in Phys Rev D 97:115023, 2018) we explored a prospect of discovering the heavy Majorana right-handed neutrinos (RHNs) at the future LHC in the context of the minimal non-exotic U(1) extended Standard Model (SM), where a pair of RHNs are created via decay of resonantly produced massive U(1) gauge boson ( ({Z}^{\prime }) ). We have pointed out that this model can yield a significant enhancement of the branching ratio of the ({Z}^{\prime }) boson to a pair of RHNs, which is crucial for discovering the RHNs under the very severe LHC Run-2 constraint from the search for the ({Z}^{\prime }) boson with dilepton final states. In this paper, we perform a general parameter scan to evaluate the maximum production rate of the same-sign dilepton final states (smoking gun signature of Majorana RHNs production) at the LHC, while reproducing the neutrino oscillation data. We also consider the minimal non-exotic U(1) model with an alternative charge assignment. In this case, we find a further enhancement of the branching ratio of the ({Z}^{\prime }) boson to a pair of RHNs compared to the conventional case, which opens up a possibility of discovering the RHNs even before the ({Z}^{\prime }) boson at the future LHC experiment.