Protonic ceramic fuel cells (PCFCs) offer a convenient means for electrochemical conversion of chemical energy into electricity at intermediate temperatures with very high efficiency. Although BaCeO₃- and BaZrO₃-based complex oxides have been positioned as the most promising PCFC electrolytes, the design of new protonic conductors with improved properties is of paramount importance. Within the present work, we studied transport properties of scandium-doped barium stannate (Sc-doped BaSnO₃). Our analysis included the fabrication of porous and dense BaSn_1-xSc_xO_3-δ ceramic materials (0 ≤ x ≤ 0.37), as well as a comprehensive analysis of their total, ionic, and electronic conductivities across all the experimental conditions realized under the PCFC operation: both air and hydrogen atmospheres with various water vapor partial pressures (p(H₂O)), and a temperature range of 500-900 ℃. This work reports on electrolyte domain boundaries of the undoped and doped BaSnO₃ for the first time, revealing that pure BaSnO₃ exhibits mixed ionic-electronic conduction behavior under both oxidizing and reducing conditions, while the Sc-doping results in the gradual improvement of ionic (including protonic) conductivity, extending the electrolyte domain boundaries towards reduced atmospheres. This latter property makes the heavily-doped BaSnO₃ representatives attractive for PCFC applications.