We examine theoretical features of U(1) X extensions of the Standard Model whose quantum anomalies are canceled per generation. Similarly to other versions, the theory consists of a Two-Higgs-Doublet Model plus a scalar singlet embedded into the SM ⊗ U(1) X gauge group, and introduces small modifications to the Z-boson interactions. These changes can be minimized by exclusively charging right-handed fermions under the new Abelian symmetry, and are compensated by the neutral X-boson exchange. Nonuniversality of fermion couplings can also be achieved by requiring one single X-charged family. In general, X gauge bosons can be separated into A and Z subsets, distinguished by the presence of axial-vector components in the Z exchange. A physics, in particular the dark photons case, is commonly simpler to constrain and therefore favored by experimental tests. Finally, the model can be UV completed both by stable χ fermions or by right-handed neutrinos. The prior case may provide cold WIMPs in the theory.