An analytical and numerical study has been carried out for the generation of terahertz (THz) radiation by beating of two intense cosh-Gaussian laser beams (decentered Gaussian beams) in the rippled density magnetized plasma under the relativistic–ponderomotive regime. In this process, both laser beams exert a relativistic–ponderomotive force on plasma electrons at the beat frequency and impart them an oscillatory velocity in the presence of a static magnetic field. Due to coupling between this nonlinear oscillatory velocity with density ripple, nonlinear current is generated that excites the THz radiation at the different frequency. Higher-order paraxial-ray approximation (non-paraxial theory) has been used in this study. The effects of the decentered parameter, magnetic field, and density ripple on the THz radiation generation in ripple density magnetized plasma have been investigated. Further, the effect of beating of laser beams on the THz field amplitude and the efficiency of THz radiation have been studied. The amplitude and efficiency of the emitted radiation are found to be highly sensitive to the decentered parameter, magnetic field, and density ripple. It has been found that the amplitude and efficiency of the generated THz radiation increase significantly with increasing the values of decentered parameter, magnetic field, and density ripple.