Kesterite Cu2ZnSnS4 (CZTS) is regarded as one of the most promising materials for thin-film solar cells due to its high light absorption capability, composition of earth-abundant and nontoxic elements, and ease of low-cost mass production. Although the certified power conversion efficiency (PCE) of kesterite solar cells has exceeded 14%, this efficiency remains significantly below the Shockley-Queisser limit. In this study, we generated a Perdew-Burke-Ernzerhof (PBE) band gap data set encompassing 263 64-atom species for high-throughput screening by substituting elements at different sites in A2BCX4 quaternary kesterite materials. Additionally, we utilized a symbolic regression method based on genetic programming to explore the functional relationship among the oxidation state, ionic radius, and electronegativity of kesterites with PBE band gaps. Simultaneously, we employed decision tree models (XGBoost, LightGBM, CatBoost, and random forest) and convolutional neural network (CNN) models (CustomCNN, VGG16, DenseNet121, Xception, and EfficientNetV2B0) to predict band gaps, achieving a coefficient of determination (R2) of up to 0.93. Furthermore, we selected 54 kesterite materials with PBE band gaps ranging from 0.4 to 1.5 eV for detailed electronic structure calculations with Heyd-Scuseria-Ernzerhof (HSE06) functional and investigated the effects of B-site atomic substitutions on the performance of solar cell materials. Compared to Ag2CaSnSe4, Ag2SrSnSe4 exhibits fewer deep defects and richer shallow defects, which contribute to an increased carrier concentration and reduced charge and energy losses, making it a superior candidate for solar cell applications.