We study the Josephson effect in a quantum spin Hall system coupled to a
localized magnetic impurity. As a consequence of the fermion parity anomaly,
the spin of the combined system of impurity and spin-Hall edge alternates
between half-integer and integer values when the superconducting phase
difference across the junction advances by 2π. This leads to characteristic
differences in the splittings of the spin multiplets by exchange coupling and
single-ion anisotropy at phase differences, for which time-reversal symmetry
is preserved. We discuss the resulting 8π-periodic (or Z4) fractional
Josephson effect in the context of recent experiments
