The generation of radicals through photo-Fenton-like reactions demonstrates significant potential for remediating emerging organic contaminants (EOCs) in complex aqueous environments. However, the excitonic effect, induced by Coulomb interactions between photoexcited electrons and holes, reduces carrier utilization efficiency in these systems. In this study, we develop Cu single-atom-loaded covalent organic frameworks (Cu_SA/COFs) as models to modulate excitonic effects. Temperature-dependent photoluminescence and ultrafast transient absorption spectra reveal that incorporating acenaphthene units into the linker (Cu_SA/Ace-COF) significantly reduces exciton binding energy (E_b). This modification not only enhances peroxymonosulfate adsorption at Cu active sites but also facilitates rapid electron transfer and promotes selective hydroxyl radical generation. Compared to Cu_SA/Obq-COF (E_b = 25.6 meV), Cu_SA/Ace-COF (E_b = 12.2 meV) shows a 39.5-fold increase in the pseudo-first-order rate constant for sulfamethoxazole degradation (0.434 min⁻¹). This work provides insights into modulating excitonic behavior in single-atom catalysts via linker engineering for EOCs degradation.