Dark matter-electron scattering and freeze-in scenarios in the light of Z^ mediation

We investigate dark matter (DM)-electron scattering in a minimal U(1)X extension of the Standard Model (SM), where the DM can appear as a Majorana fermion, a complex singlet scalar or a Dirac fermion. To study bounds on the U(1)X gauge coupling (gX) and new gauge boson mass (MZ⁾, from DM-electron scattering, we consider several direct search experiments like CDMS, DAMIC, SENSEI, PandaX-II, DarkSide-50 and XENON1T-S2 for different U(1)X charges. In this set-up we consider DM production via freeze-in both in radiation dominated and modified cosmological background to project sensitivities on gX-MZ^ plane satisfying observed relic abundance. DM-electron scattering could provide comparable, or even stronger bounds than those obtained from the electron/ muon $(g-2)$, low energy scattering and intensity frontier experiments within 0.01 GeV MZ^ 0.1 GeV. Constrains from freeze-in could provide stronger sensitivities for MZ^ O(1) GeV, however, these limits are comparable to those obtained from LHCb, LEP experiments for O(10) GeV MZ^ 150 GeV. In future, electron-muon scattering (MUonE), proton (FASER, DUNE) and electron/positron (ILC) beam dump experiments could probe these parameters.