  We theoretically study Josephson junctions with a transition metal
dichalcogenide zigzag ribbon as a weak link. We demonstrate that the spatial
profile of the supercurrent carried by the edge modes determines the critical
current dependence on the perpendicular magnetic field. We explore this finding
and analyze the impact of Zeeman interaction and the orbital effects of the
magnetic field on the Andreev bound states energies. We show that the unequal
Fermi velocities of the spin-opposite edge modes lead to an anomalous shift of
the Andreev bound states in the presence of the magnetic field. This is
manifested in a pronounced modification of the SQUID critical current
oscillations when two opposite edges of the ribbon are conducting and can be
exploited in order to reveal the anomalous phase shift of the Andreev bound
states in a single Josephson junction device.
