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We demonstrate that a correlated equilibrium $f$-electron system withtime-reversal symmetry can exhibit a $\mathbb{Z}_2$ non-Hermitian skin effectof quasi-particles. In particular, we analyze a two-dimensional periodicAnderson model with spin-orbit coupling by combining the dynamical mean-fieldtheory (DMFT) and the numerical renormalization group. We prove the existenceof the $\mathbb{Z}_2$ skin effect by explicitly calculating the topologicalinvariant and show that spin-orbit interaction is essential to this effect. OurDMFT analysis demonstrates that the $\mathbb{Z}_2$ skin effect ofquasi-particles is reflected on the pseudo-spectrum. Furthermore, we analyzetemperature effects on this skin effect using the generalized Brillouin zonetechnique, which clarifies that the skin modes are strongly localized above theKondo temperature.

$\mathbb{Z}_2$ Non-Hermitian skin effect in equilibrium heavy-fermions