<p>In this study, we analyze the impact of external magnetic field on laser wakefield acceleration (LWFA) driven by cosine-Gaussian laser pulse in homogeneous plasma. The unique characteristics of cosine-Gaussian pulses provide an alternative to the more commonly studied Gaussian pulses in LWFA applications. By introducing an external magnetic field, we aim to explore dynamics of plasma wake formation and its impact on electron acceleration. Our investigation begins with a theoretical framework for the cosine-Gaussian laser pulse-plasma medium interaction under different magnetic field strengths. We use analytical models to study and evaluate laser wakefield structure, laser wake potential, laser wakefield and electron energy gain. Simulations conducted using MATHEMATICA software demonstrate that a magnetic field has the capacity to amplify plasma waves, resulting in increased acceleration efficiency depending on field orientation and strength. We also investigate the parametric dependencies of the wakefield modifications, including the effects of laser intensity, pulse length and plasma density. This research provides new insights into the controllability of LWFA processes through external magnetic fields and demonstrates the potential of cosine-Gaussian pulse lasers in advanced particle acceleration applications.</p>