We theoretically investigate a tunable and suppressible non-Hermitian skin effect (NHSE) in lattice systems governed by non-Abelian SU(2) gauge fields, Zeeman field, and spin-dependent gain and loss. We show that non-Abelian hopping alone can generate a parity-dependent discrepancy between open- and periodic-boundary spectra, even in the absence of the NHSE. A uniform Zeeman field or spin-dependent gain and loss activates a direction-selective NHSEs, whereas their coexistence gives rise to a bipolar NHSE. Strikingly, we find that a spatially nonuniform Zeeman field generically suppresses the NHSE and drives boundary-accumulated skin modes back into the bulk, irrespective of the modulation profile. This suppression originates from the competition between skin-induced boundary accumulation and gradient-induced Wannier–Stark-like localization. Our results reveal versatile and experimentally accessible mechanisms for engineering, tuning, and suppressing non-Hermitian boundary localization, and provide a promising route toward exploring non-Abelian non-Hermitian physics in platforms such as electrical circuits.

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• Density of states
• Skin effect
• Zeeman effect
• Non-Hermitian systems
• Tight-binding model