This study was aimed to reduce the production cost of fungal exopolysaccharides by increasing the yield and extracting chitosan from the fungal wastes produced simultaneously. Aspergillus quadrilineatus was isolated as well as identified morphologically and by molecular analyses (GenBank Accession No. MT742630.1). One-variable-at-a-time method was combined with response surface methodology to explore the effects of medium components and fermentation conditions on both exopolysaccharide and biomass yields. Sucrose and the inorganic nitrogen (NH4)2SO4 had the greatest stimulating effect on biomass and exopolysaccharide production. The highest biomass and exopolysaccharide production were found after 14 and 4 days of fermentation, respectively. Statistical analyses of Plackett–Burman experimental design indicated that the models were significant, in particular, (NH4)2SO4, K2HPO4, tween 80, CaCl2.2H2O, sucrose, and the incubation interval were the most significant for exopolysaccharide production and biomass. Responses of the central composite design for biomass and exopolysaccharide production cleared the strong similarity between the experimental and predicted values. The optimized medium boosted the exopolysaccharide by 329.73% and the biomass by 31.44% of the primary yield. The waste fungal biomass, obtained after production of the enhanced exopolysaccharide, was used to extract chitosan, yielding 3.52 mg/g with about 88.84% deacetylation degree (DD).