  In this work, we have obtained the solutions of a massless fermion which is
under the external magnetic field around a cosmic string for specific three
potential models using supersymmetric quantum mechanics. The constant magnetic
field, energy dependent potentials and position dependent mass models are
investigated for the Dirac Hamiltonians and an extension of these three
potential models and their solutions are also obtained. The energy spectrum and
potential graphs for each case are discussed for the $\alpha$ deficit angle.
