We examine the electron dynamics during laser-cluster interaction. In addition to the electrostatic field of an individual cluster and laser field, we consider an external transverse wiggler magnetic field, which plays a pivotal role in enhancing the electron acceleration. Single-particle simulation has been presented with a short pulse linearly polarized as well as circularly polarized laser pulses for electron acceleration in a cluster. The persisting Coulomb field allows the electron to absorb energy from the laser field. The stochastically heated electron finds a weak electric field at the edge of the cluster from where it is ejected. The wiggler magnetic field connects the regions of the stochastically heated, ejected electron from the cluster and high energy gain by the electron from the laser field outside the cluster. This increases the field strength and hence supports the electron to meet the phase of the laser field for enhanced acceleration. A long duration resonance appears with an optimized magnetic wiggler field of about 3.4 kG. Hence, the relativistic energy gain by the electron is enhanced up to a few 100 MeV with an intense short pulse laser with an intensity of about 1019 W cm−2 in the presence of a wiggler magnetic field.