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~$\rm fb^{-1}$.