  Junctions created by coupling two superconductors via a semiconductor
nanowire in the presence of high magnetic fields are the basis for detection,
fusion, and braiding of Majorana bound states. We study NbTiN/InSb
nanowire/NbTiN Josephson junctions and find that their critical currents in the
few mode regime are strongly suppressed by magnetic field. Furthermore, the
dependence of the critical current on magnetic field exhibits gate-tunable
nodes. Based on a realistic numerical model we conclude that the Zeeman effect
induced by the magnetic field and the spin-orbit interaction in the nanowire
are insufficient to explain the observed evolution of the Josephson effect. We
find the interference between the few occupied one-dimensional modes in the
nanowire to be the dominant mechanism responsible for the critical current
behavior. The suppression and non-monotonic evolution of critical currents at
finite magnetic field should be taken into account when designing circuits
based on Majorana bound states.
