Resonant enhancement in electron acceleration due to a circularly polarized laser pulse in plasma, under the combined influence of external azimuthal and axial magnetic fields, is studied. We have investigated direct electron acceleration in plasma by employing a relativistic single particle simulation. The plasma is magnetized with an azimuthal magnetic field applied in the perpendicular plane and an axial magnetic field applied along the direction of laser beam propagation. Resonance takes place between electron and electric field of the laser pulse for the optimum value of the combined magnetic field, which supports electron acceleration to higher energies, up to the betatron resonance point. The optimum value of these magnetic fields is highly sensitive to laser initial intensity and laser initial spot size. The effects of laser intensity, initial spot size, and laser pulse duration are taken into consideration in optimizing the magnetic field for efficient electron acceleration. Higher electron energy gain, of the order of GeV, is observed by employing terawatt circularly polarized laser pulses in plasma under the influence of combined magnetic field of about 10 MG.