We analyse how dark matter (DM) can be produced in the early universe, working in the framework of a hidden sector charged under a U(1)' gauge symmetry and interacting with the Standard Model through kinetic mixing. Depending on the masses of the dark matter particle and of the dark photon, as well as on the hidden U(1)' gauge coupling and the kinetic mixing parameter, we classify all the distinct regimes along which the observed dark matter relic density can be accounted for. We find that 9 regimes are potentially operative to produce the DM particles and this along 5 distinct dynamical mechanisms. Among these, 4 regimes are new and correspond to regimes in which the DM particles are produced by on-shell dark photons. One of them proceeds along a new dynamical mechanism, which we dub sequential freeze-in. We argue that such regimes and the associated dynamical mechanisms are characteristic of DM models for which, on top of the Standard Model and the dark sector, there are other massive, but relatively light particles -- akin to the dark photon -- that interact both with the SM and the DM sectors.

18 pages, 14 figures