  We generalize previous results for the superplane Landau model to exhibit an
explicit worldline N = 2 supersymmetry for an arbitrary magnetic field on any
two-dimensional manifold. Starting from an off-shell N = 2 superfield
formalism, we discuss the quantization procedure in the general case
characterized by two independent potentials on the manifold and show that the
relevant Hamiltonians are factorizable. In the restricted case when both the
Gauss curvature and the magnetic field are constant over the manifold and, as a
consequence, the underlying potentials are related, the Hamiltonians admit
infinite series of factorization chains implying the integrability of the
associated systems. We explicitly determine the spectrum and eigenvectors for
the particular model with CP^1 as the bosonic manifold.
