  We show that Dirac fermions moving in two spatial dimensions with a
generalized dispersion $E\sim p^N$, subject to an external magnetic field and
coupled to a complex scalar field carrying a vortex defect with winding number
$Q$ acquire $NQ$ zero modes. This is the same as in the absence of the magnetic
field. Our proof is based on selection rules in the Landau level basis that
dictate the existence and the number of the zero modes. We show that the result
is insensitive to the choice of geometry and is naturally extended to general
field profiles, where we also derive a generalization of the Aharonov-Casher
theorem. Experimental consequences of our results are briefly discussed.
