  We study a mesoscopic superconducting ring threaded by a magnetic flux when
the single particle level spacing is not negligible. It is shown that, for a
superconducting ring with even parity, the behavior of persistent current is
equivalent to what is expected in a bulk superconducting ring. On the other
hand, we find that a ring with odd parity shows anomalous behavior such as
fluxoid quantization at half-integral multiples of the flux quantum and
paramagnetic response at low temperature. We also discuss how the parity effect
in the persistent current disappears as the temperature is raised or as the
size of the ring increases.
