The contemporary theoretical investigation researches the resonant emission of high-energy gamma-quanta within the process of scattering of ultrarelativistic electrons on a nucleus in the external electromagnetic field. With implementation of the resonant conditions under the field ambience the particle in the intermediate state re-modulates into the real form. Therefore, the phenomenon examination determines the functional splitting of the second order process into a pair of first-order effects that possess a possibility to develop within two reaction channels. Consequently, the first channel characterizes the kinematics of electron scattering by a nucleus and following radiation of a spontaneous gamma-quantum. The second channel delineates the spontaneous gamma-quantum radiation by an electron with subsequent scattering on a nucleus. It is important to emphasize that within a specific range of observation the calculations derive three discrete magnitudes for the resonant frequency dependency on the angle of spontaneous photon radiation. As a result, the work represents an estimation of the resonant differential scattering cross-section in ratio to the scattering cross-section computed without the external field. In conclusion, various scientific facilities may verify the project data simulation (SLAC, FAIR, XFEL, ELI, XCELS).