  The Standard Model effective field theory (SMEFT) provides a general
framework to include the dynamics of the beyond standard model physics residing
at a certain higher energy scale $\Lambda$. We study the top-quark production
along with a Higgs boson and a jet (tHq) at the LHC experiment within the
framework of the SMEFT. First, identifying the relevant sensitive dimension-6
SMEFT operators, a strategy is developed to constrain the Wilson Coefficients
(WC) corresponding to these associated SMEFT operators using the latest LHC
measurements, providing a complementary way to the global-fit approach. The
best-fit values of these WCs are presented. Finally, we discuss the discovery
potential of the signatures of those operators. We find that a discoverable
excess due to SMEFT effects can be observed in the tHq process at the LHC with
the center of mass energy $\sqrt{s}=13$ TeV and integrated luminosity options
${\cal L}=$300 $\rm fb^{-1}$ and 3000 $\rm fb^{-1}$.
