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Our main aim in this paper is to constrain the effective field theorydescribing the top quark couplings through the $e^{-} e^{+} \rightarrow t\bar{t}+$jet process. The analysis is carried out considering two differentcenter-of-mass energies of 500 and 3000 GeV including a realistic simulation ofthe detector response and the main sources of background processes. Theexpected limits at 95\% CL are derived on the new physics couplings such as $t\bar t \gamma$, $t \bar t Z$, and $t \bar t g$ for each benchmark scenariousing the dileptonic $t \bar{t}$ final state. We show that the 95\% CL limitson dimensionless Wilson coefficients $\bar{c}_i$ considered in this analysiscould be probed down to $10^{-4}$.

Constraining the top quark effective field theory using the top quark pair production in association with a jet at future lepton colliders