The presence of an axial magnetic field in a laser beat wave accelerator enhances the oscillatory velocity of electrons due to cyclotron resonance effect leading to higher amplitude of the ponderomotive force driven plasma wave, and higher energy of accelerating electrons. The axial magnetic field inhibits the transverse escape of electrons and thus causes a growth of the interaction length. The surfatron acceleration of electrons also shows a similar enhancement. A surfatron transverse magnetic field deflects the electrons parallel to the phase fronts of the accelerating wave keeping them in phase with it. However, the electron continues to move away radially.