A search for the production of a top quark in association with a photon and additional jets via flavor changing neutral current interactions is presented. The analysis uses proton-proton collision data recorded by the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138  fb⁻¹. The search is performed by looking for processes where a single top quark is produced in association with a photon, or a pair of top quarks where one of the top quarks decays into a photon and an up or charm quark. Events with an electron or a muon, a photon, one or more jets, and missing transverse momentum are selected. Multivariate analysis techniques are used to discriminate signal and standard model background processes. No significant deviation is observed over the predicted background. Observed (expected) upper limits are set on the branching fractions of top quark decays: ℬ⁡(𝑡→𝑢⁢𝛾)<0.95×10⁻⁵ (1.20×10⁻⁵) and ℬ⁡(𝑡→𝑐⁢𝛾)<1.51×10⁻⁵ (1.54×10⁻⁵) at 95% confidence level, assuming a single nonzero coupling at a time. The obtained limit for ℬ⁡(𝑡→𝑢⁢𝛾) is similar to the current best limit, while the limit for ℬ⁡(𝑡→𝑐⁢𝛾) is significantly tighter than previous results.