We investigate localization and the non-Hermitian skin effect in a one-dimensional nonreciprocal chain with unidirectional Aubry-André-Harper hopping. The interplay between nonreciprocity and quasiperiodic modulation produces rich localization behavior, including transitions among extended, critical, and localized regimes, reentrant localization, and an energy-dependent skin effect. We show that the global skin effect can be suppressed, reversed, and restored by tuning the quasiperiodic strength, which also drives a pseudo-Hermitian transition in the band structure. By analyzing participation ratios, wave-function distributions, and complex-energy spectra under periodic and open boundary conditions, we further demonstrate that spectral reconstruction provides a clear signature of the skin effect. In addition, extending the eigenspectrum to the complex plane in a ring geometry reveals a localization transition of complex-energy modes analogous to Anderson localization. These results show that unidirectional quasiperiodic hoppings offer a versatile route to controlling localization and skin physics in non-Hermitian systems.

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• Anderson localization
• Skin effect
• Non-Hermitian systems