  Charge conserving spin singlet and spin triplet superconductors in one
dimension are described by the $U(1)$ symmetric Thirring Hamiltonian. We solve
the model with open boundary conditions on the a finite line segment by means
of the Bethe Ansatz. We show that the ground state displays a fourfold
degeneracy when the bulk is in the spin triplet superconducting phase. This
degeneracy corresponds to the existence of zero energy boundary bound states
localized at the edges which may be interpreted, in the light of the previous
semi-classical analysis due to Kesselman and Berg \cite{Keselman2015}, as
resulting from the existence of fractional spin $\pm 1/4$ localized at the two
edges of the system.
