Terrestrial gamma‐ray flashes (TGFs) are beams of high‐energy photons associated to lightning. These photons are the bremsstrahlung of energetic electrons whose origin is currently explained by two mechanisms: energizing electrons in weak, but large‐scale thundercloud fields or the acceleration of low‐energy electrons in strong, but localized fields of lightning leaders. Contemporary measurements by the Atmosphere‐Space Interactions Monitor suggest that the production of TGFs is related to the leader step and associated streamer coronae when upwards moving intracloud lightning illuminates. Based on these observations, we apply a particle‐in‐cell Monte Carlo code tracing electrons in the superposed electric field of two encountering streamer coronae and modeling the subsequent photon emission. We also perform a parameter study by solving the deterministic equations of motion for one electron. We find that this mechanism can explain the occurrence of TGFs with photons energies of several MeV lasting for 10s to 100s of μs, in agreement with observations.