Cation substitution plays a crucial role in improving the efficiency of Cu₂ZnSn(S,Se)₄ (CZTSSe) solar cells. In this work, we report a significant efficiency enhancement of flexible CZTSSe solar cells on Mo foils by partial substitution of Cu⁺ with Ag⁺. It is found that the band gap (E_g) of (Cu_1−xAg_x)₂ZnSn(S,Se)₄ (CAZTSSe) thin films can be adjusted by doping with Ag with x from 0 to 6%, and the minimum E_g is achieved with x = 5%. We also found that Ag doping can obviously increase the average grain size of the CAZTSSe absorber from 0.4 to 1.1 μm. Additionally, the depletion width (W_d) at the heterojunction interface of CAZTSSe/CdS is found to be improved. As a result, the open-circuit voltage deficit (V_oc,def) is gradually decreased, and the band tailing is suppressed. Benefiting from the enhanced open-circuit voltage (V_oc), the power conversion efficiency (PCE) is successfully enhanced from 4.34% (x = 0) to 6.24% (x = 4%), and the V_oc,def decreases from 915 to 848 mV.