  This article provides the calculation of an effective vertex function between
a nucleon and a $Z^\prime$ boson that couples preferentially to either the top
quark or the third generation of fermions, for the purpose of calculating
vector-portal dark matter nuclear recoil cross sections. Mixing effects between
the new gauge group $U(1)^\prime$ and the Standard Model hypercharge group
$U(1)_Y$ are taken into account. Contributions to the $U(1)^\prime$ nucleon
current from heavy quarks are quantified using the heavy quark expansion. Also
taken into account are contributions from the 1-loop $Z^\prime$-gluon
interactions and mixing-induced contributions from the light quarks in the
nucleon. We find that, for reasonable values of the $U(1)^\prime$ gauge
parameter, contributions from the light quarks dominate despite being
mixing-suppressed. It is shown that this holds for most models even if mixing
effects do not appear at tree level. Contributions from the heavy quarks and
gluons are suppressed by $1/m_Q^2$ and possibly also by momentum in the low
momentum transfer limits relevant for dark matter direct detection. We discuss
under which conditions the subdominant terms become relevant.
