  The quantum nonrelativistic spin-1/2 planar systems in the presence of a
perpendicular magnetic field are known to possess the N=2 supersymmetry. We
consider such a system in the field of a magnetic vortex, and find that there
are just two self-adjoint extensions of the Hamiltonian that are compatible
with the standard N=2 supersymmetry. We show that only in these two cases one
of the subsystems coincides with the original spinless Aharonov-Bohm model and
comes accompanied by the super-partner Hamiltonian which allows a singular
behavior of the wave functions. We find a family of additional, nonlocal
integrals of motion and treat them together with local supercharges in the
unifying framework of the tri-supersymmetry. The inclusion of the dynamical
conformal symmetries leads to an infinitely generated superalgebra, that
contains several representations of the superconformal osp(2|2) symmetry. We
present the application of the results in the framework of the two-body model
of identical anyons. The nontrivial contact interaction and the emerging N=2
linear and nonlinear supersymmetries of the anyons are discussed.
