In this paper, we theoretically investigated the influence of externally applied fields such as high-frequency non-resonant intense laser fields, static electric and magnetic fields, as well as structure parameters, on the interband transitions and exciton binding energy of a GaAs quantum well with Razavy confinement potential. To perform numerical calculations, the ground state electron and heavy hole subband energy levels of the structure and the envelope wave functions corresponding to these states were calculated using a variational method within the framework of the effective mass and parabolic band approaches. After obtaining the numerical values, the band transitions of the structure, the exciton binding energy, the dipole moment matrix elements, and the transition energy between the ground state electron and heavy hole subband energies of the structure were evaluated in detail. The results show that the Razavy potential profile turns into a single QW structure for particular dimensionless structure parameters and the peak position of the interband transition coefficient shifts toward red (lower energy) with the increase in the structure parameters and electric field strength, while it shifts toward the blue (higher energy) with the increase in the intensity of the intense laser field and magnetic field. We believe that these numerical results will be useful in the design and production of next-generation electronic and optoelectronic devices.