  We investigate the effects of magnetic field on a charged fermion in a
$(1+2)$-dimensional wormhole. Applying external magnetic field along the axis
direction of the wormhole, the Dirac equation is set up and analytically solved
in two scenarios, constant magnetic flux and constant magnetic field through
the throat of the wormhole. For the constant magnetic flux scenario, the system
can be solved analytically and exact solutions are found. For the constant
magnetic field scenario, with the short wormhole approximation, the quantized
energies and eigenstates are obtained. The system exhibits both the spin-orbit
coupling and the Landau quantization for the stationary states in both
scenarios. The intrinsic curvature of the surface induces the spin-orbit and
spin-magnetic Landau couplings that generate imaginary energy. Imaginary energy
can be interpreted as the energy dissipation and instability of the states.
Generically, the states of charged fermion in wormhole are quasinormal
modes~(QNMs) that could be unstable for positive imaginary frequencies and
decaying for negative imaginary ones. For the constant flux scenario, the
fermions in the wormhole can behave like bosons and have arbitrary statistics
depending on the flux. We also discuss the implications of our results in the
graphene wormhole system.
