  Harnessing spin and parity degrees of freedom is of fundamental importance
for the realization of emergent quantum devices. Nanostructures embedded in
superconductor--semiconductor hybrid materials offer novel and yet unexplored
routes for addressing and manipulating fermionic modes. Here we
spectroscopically probe the two-dimensional band structure of Andreev bound
states in a phase-controlled hybrid three-terminal Josephson junction. Andreev
bands reveal spin-degeneracy breaking, with level splitting in excess of 9 GHz,
and zero-energy crossings associated to ground state fermion parity
transitions, in agreement with theoretical predictions. Both effects occur
without the need of external magnetic fields or sizable charging energies and
are tuned locally by controlling superconducting phase differences. Our results
highlight the potential of multiterminal hybrid devices for engineering quantum
states.
