The present calculations show that the application of an external magnetic field can generate additional component of the wakefield suitable for Terahertz (THz) radiation generation in a collisional plasma. Based on the approach of perturbation technique under quasi-static approximation, a study is made on the field of emitted radiation pulses from the wakefield when the super-Gaussian laser beams are used. The field of the radiation becomes stronger when stronger magnetic field is applied and the same is the case for the lasers of higher index.