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Abstract A search is presented for the pair production of new heavy resonances, each decaying into a top quark (t) or antiquark and a gluon (g). The analysis uses data recorded with the CMS detector from proton–proton collisions at a center-of-mass energy of 13$$\,\text {Te}\hspace{-.08em}\text {V}$$ $\text{Te}\text{V}$at the LHC, corresponding to an integrated luminosity of 138$$\,\text {fb}^{-1}$$ ${\text{fb}}^{-1}$. Events with one muon or electron, multiple jets, and missing transverse momentum are selected. After using a deep neural network to enrich the data sample with signal-like events, distributions in the scalar sum of the transverse momenta of all reconstructed objects are analyzed in the search for a signal. No significant deviations from the standard model prediction are found. Upper limits at 95% confidence level are set on the product of cross section and branching fraction squared for the pair production of excited top quarks in the$$\text {t}^{*} \rightarrow {\text {t}} {\text {g}} $$ $\text{t}_{}^{\ast }\to \text{tg}$decay channel. The upper limits range from 120 to 0.8$$\,\text {fb}$$ $\text{fb}$for a$$\text {t}^{*} $$ $\text{t}_{}^{\ast }$with spin-1/2 and from 15 to 1.0$$\,\text {fb}$$ $\text{fb}$for a$$\text {t}^{*} $$ $\text{t}_{}^{\ast }$with spin-3/2. These correspond to mass exclusion limits up to 1050 and 1700$$\,\text {Ge}\hspace{-.08em}\text {V}$$ $\text{Ge}\text{V}$for spin-1/2 and spin-3/2$$\text {t}^{*} $$ $\text{t}_{}^{\ast }$particles, respectively. These are the most stringent limits to date on the existence of$$\text {t}^{*} \rightarrow {\text {t}} {\text {g}} $$ $\text{t}_{}^{\ast }\to \text{tg}$resonances.