  We consider the generic scalar potential with CP-violation, and study the $Z$
resonance and inelastic dark matter in the Simple Extension of the Standard
Model (SESM), which can explain the dark matter as well as new physics
anomalies such as the B physics anomalies and muon anomalous magnetic moment,
etc. With the new scalar potential terms, we obtain the mass splittings for the
real and imaginary parts of scalar fields. And thus we can have the DM
co-annihilation process mediated by $Z$ boson, which couples exclusively to the
CP-even and CP-odd parts of scalar fields. This is a brand new feature compared
to the previous study. For the CP conserving case, we present the viable
parameter space for the Higgs and $Z$ resonances, which can explain the B
physics anomalies, muon anomalous magnetic moment, and dark matter relic
density, as well as evade the constraint from the XENON1T direct detection
simultaneously. For the CP-violating case, we consider the inelastic dark
matter, and study four concrete scenarios for the inelastic DM-nucleon
scatterings mediated by the Higgs and $Z$ bosons in details. Also, we present
the benchmark points which satisfy the aforementioned constraints. Furthermore,
we investigate the constraints from the dark matter-electron inelastic
scattering processes mediated by the Higgs and $Z$ bosons in light of the
XENONnT data. We show that the constraint on the $Z$ mediated process is weak,
while the Higgs mediated process excludes the dark matter with mass around
several MeV.
