How dark is the $ u_R$-philic dark photon?

We consider a generic dark photon that arises from a hidden $U(1)$ gauge symmetry imposed on right-handed neutrinos ($ u_{R}$). Such a $ u_{R}$-philic dark photon is naturally dark due to the absence of tree-level couplings to normal matter. However, loop-induced couplings to charged leptons and quarks are inevitable, provided that $ u_{R}$ mix with left-handed neutrinos via Dirac mass terms. We investigate the loop-induced couplings and find that the $ u_{R}$-philic dark photon is not inaccessibly dark, which could be of potential importance to future dark photon searches at SHiP, FASER, Belle-II, LHC 14 TeV, etc.