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Abstract In this paper we investigate the phenomenology of the U(1) gauge symmetry for right-handed fermions, where three right-handed neutrinos are introduced for anomalies cancellations. Constraints on the new gauge boson $$Z_{\mathbf {R}}$$ ZR from $$Z-Z^\prime $$ Z-Z′ mixing as well as the upper bound of $$Z^\prime $$ Z′ production cross section in di-lepton channel at the LHC are presented. We further study the neutrino mass and the phenomenology of $$Z_{\mathbf {R}}$$ ZR -portal dark matter in this model. The lightest right-handed neutrino can be the cold dark matter candidate stabilized by a $$Z_2$$ Z2 flavor symmetry. Our study shows that active neutrino masses can be generated via the modified type-II seesaw mechanism; right-handed neutrino is available dark matter candidate for its mass being very heavy, or for its mass at near the resonant regime of the SM Higgs and(or) the new bosons; constraint from the dilepton search at the LHC is stronger than that from the $$Z-Z^\prime $$ Z-Z′ mixing only for $$g_\mathbf {R}<0.121$$ gR<0.121 , where $$g_\mathbf {R}$$ gR is the new gauge coupling.