This research reports the increased electron energy gain from laser wakefield acceleration in density-modulated plasma with an external magnetic field. Periodic plasma density- modulation can excite higher harmonics of different phase velocities of fundamental wakefield that can assist in improving the self-trapping of pre-accelerated electrons to accelerate them for higher energy. Furthermore, the applied magnetic field assisted self-injection can also contribute in electron energy enhancement during the acceleration. The physical mechanism is described with a theoretical formulation for this scheme. Results of two-dimensional particle-in-cell simulations are reported to understand the proposed idea.