We investigate the topological properties of a Josephson junction obtained by constraining a two-dimensional electron gas at the oxide interface to form a quasi-one-dimensional conductor. We reveal an anomalous critical current behavior with a magnetic field applied perpendicular to the Rashba spin-orbit one. We relate the observed critical current enhancement at small magnetic fields with the appearance of orbital-flavored Majorana bound states (OMBSs) pinned at the edges of the superconducting leads. Signatures of OMBSs also include a sawtooth profile in the current-phase relation. Our findings allow us to recognize fingerprints of topological superconductivity in noncentrosymmetric materials and confined systems with a spin-orbit interaction. They also explain recent experimental observations for which a microscopic description is still lacking.
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