  We investigate fermionic dark matter interactions with standard model
particles from an additional $\mathrm{U}(1)_\mathrm{X}$ gauge symmetry,
assuming kinetic mixing between the $\mathrm{U}(1)_\mathrm{X}$ and
$\mathrm{U}(1)_\mathrm{Y}$ gauge fields as well as a nonzero
$\mathrm{U}(1)_\mathrm{X}$ charge of the Higgs doublet. For ensuring
gauge-invariant Yukawa interactions and the cancellation of gauge anomalies,
the standard model fermions are assigned $Y$-sequential
$\mathrm{U}(1)_\mathrm{X}$ charges proportional to the Higgs charge. Although
the Higgs charge should be small due to collider constraints, it is useful to
decrease the effective cross section of dark matter scattering off nucleons by
two orders of magnitude and easier evade from direct detection bounds. After
some numerical scans performed in the parameter space, we find that the
introduction of the Higgs charge can also enhance the dark matter relic density
by at least two orders of magnitude. When the observed relic density and the
direct detection constraints are tangled, at the case where the resonance
effect is important for dark matter freeze-out, the Higgs charge can expand
physical windows to some extent by relieving the tension between the relic
density and the direct detection.
