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 $$\,\text {Te}\hspace{-.08em}\text {V}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:mtext>Te</mml:mtext> <mml:mspace/> <mml:mtext>V</mml:mtext> </mml:mrow> </mml:math> at the LHC, corresponding to an integrated luminosity of 138 $$\,\text {fb}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:msup> <mml:mtext>fb</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . 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 $$\text {t}^{*} \rightarrow {\text {t}} {\text {g}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mtext>t</mml:mtext> <mml:mrow/> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> <mml:mo>→</mml:mo> <mml:mtext>tg</mml:mtext> </mml:mrow> </mml:math> decay channel. The upper limits range from 120 to 0.8 $$\,\text {fb}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:mtext>fb</mml:mtext> </mml:mrow> </mml:math> for a $$\text {t}^{*} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mtext>t</mml:mtext> <mml:mrow/> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> with spin-1/2 and from 15 to 1.0 $$\,\text {fb}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:mtext>fb</mml:mtext> </mml:mrow> </mml:math> for a $$\text {t}^{*} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mtext>t</mml:mtext> <mml:mrow/> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> with spin-3/2. These correspond to mass exclusion limits up to 1050 and 1700 $$\,\text {Ge}\hspace{-.08em}\text {V}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:mtext>Ge</mml:mtext> <mml:mspace/> <mml:mtext>V</mml:mtext> </mml:mrow> </mml:math> for spin-1/2 and spin-3/2 $$\text {t}^{*} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mtext>t</mml:mtext> <mml:mrow/> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> particles, respectively. These are the most stringent limits to date on the existence of $$\text {t}^{*} \rightarrow {\text {t}} {\text {g}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mtext>t</mml:mtext> <mml:mrow/> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> <mml:mo>→</mml:mo> <mml:mtext>tg</mml:mtext> </mml:mrow> </mml:math> resonances.