  Time reversal invariant topological superconducting (TRITOPS) wires are known
to host a fractional spin hbar/4 at their ends. We investigate how this
fractional spin affects the Josephson current in a TRITOPS-quantum dot-TRITOPS
Josephson junction, describing the wire in a model which can be tuned between a
topological and a nontopological phase. We compute the equilibrium Josephson
current of the full model by continuous-time Monte Carlo simulations and
interpret the results within an effective low-energy theory. We show that in
the topological phase, the 0-to-pi transition is quenched via formation of a
spin singlet from the quantum dot spin and the fractional spins associated with
the two adjacent topological superconductors.
