We theoretically investigate the interaction between azimuthal vector vortex beams and a segmented ring medium, revealing orbital-to-spin conversion in strong-field high-order harmonic generation. We show that engineered gaps in the ring target break the light-matter symmetry and mediate the transfer of the driving field's orbital angular momentum (OAM) into the spin angular momentum (SAM) of on-axis harmonic photons. The far-field harmonics exhibit alternating spin states governed by a double selection rule dependent on both gap number and relative width, reminiscent of multislit diffraction. The Fraunhofer diffraction pattern further constitutes a fingerprint of the native $n$-fold rotational symmetry in OAM-to-SAM conversion, thereby furnishing a spectroscopic diagnostic of nonlinear coupling between structured light and patterned media.

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• High-order harmonic generation
• Light-matter interaction
• Ultrafast optics