Cuprate superconductors have wide application prospects and rich physical mechanisms, attracting extensive research. However, exploring the microscopic mechanism of high-temperature superconductivity is challenging. To understand how magnetic field-induced spin fluctuations affect high-temperature superconductivity,we have investigated the Raman scattering spectra of electron-doped cuprates under external magnetic fields based on the t-t'-J model. In order to discuss the effects of different dopant concentrations and different temperatures, we calculated the Raman scattering spectra at dopant concentrations of 0.17 and 0.165 and temperatures of 0.002 J and 0.007 J. Our calculations show that with the increase of the external magnetic field, the peak intensities of B_1g and B_2g decrease significantly at different dopant concentrations and temperatures and the peak positions shift slightly to the left. This indicates that the superconducting energy gap decreases with increasing external magnetic field. In addition, the higher the temperature, the slower the rate at which the peak intensity decreases with increasing magnetic field. Our calculation results are qualitatively consistent with experiments, and provide a theoretical explanation for the Raman scattering spectra of electron-doped copper oxide superconductors under an external magnetic field.