  We demonstrate that a correlated equilibrium $f$-electron system with
time-reversal symmetry can exhibit a $\mathbb{Z}_2$ non-Hermitian skin effect
of quasi-particles. In particular, we analyze a two-dimensional periodic
Anderson model with spin-orbit coupling by combining the dynamical mean-field
theory (DMFT) and the numerical renormalization group. We prove the existence
of the $\mathbb{Z}_2$ skin effect by explicitly calculating the topological
invariant and show that spin-orbit interaction is essential to this effect. Our
DMFT analysis demonstrates that the $\mathbb{Z}_2$ skin effect of
quasi-particles is reflected on the pseudo-spectrum. Furthermore, we analyze
temperature effects on this skin effect using the generalized Brillouin zone
technique, which clarifies that the skin modes are strongly localized above the
Kondo temperature.
