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

Exploring SMEFT operators through single top-quark production associated with the Higgs boson at the LHC