Beyond the Standard Model Higgs physics: Hunting $h \rightarrow bs$ with Higgs-strahlung at CEPC and FCC-ee

The next generation of $e^{-}e^{+}$ colliders, particularly the CEPC and FCC-ee, will offer unprecedented precision to probe Higgs boson properties. In this work, we investigate the flavor-changing decay $h \rightarrow bs$ produced via Higgs-strahlung in the framework of the Two-Higgs-Doublet Model of Type III (2HDM-III). Using multivariate techniques, we project the signal significance for CEPC and FCC-ee, considering dominant backgrounds and systematic uncertainties. Our results demonstrate that these colliders could achieve $5σ$ sensitivity to $\text{BR}(h \rightarrow bs)$ down to $10^{-4}$, providing a unique window into physics beyond the Standard Model.