The incorporation of branching units in the polymer is beneficial in improving many of the polymer properties. This article deals with the synthesis of branched sulfonic acid–based copolytriazoles (PTHPSH‐XX) to prepare freestanding membranes. The copolymers were synthesized by the click reaction of 1,4‐bis(prop‐2‐ynyloxy)benzene, 1,3,5 tris[2‐trifluoromethyl‐4(4‐azidophenyl) phenoxy]benzene (B3), and 4,4′‐diazido‐2,2′‐stilbene disulfonic acid disodium salt. The chemical constructions of the subsequent copolymers were established by Fourier‐transform infrared spectroscopy and proton nuclear magnetic resonance spectroscopy. The copolymers showed high thermal stability, low water absorption, and outstanding structural robustness in their hydrated state. The presence of branching segments (B3) in the copolymers contributed to improved peroxide radical resistance and proton conductivity (71–192 mS/cm measured at 90°C) in comparison with their linear analogs. In addition, the membranes exhibited reasonably good set of mechanical properties (TS = 71–53 MPa, YM = 2.76–2.33 GPa). The membranes exhibited phase‐separated morphology in their transmission electron microscope images with ionic domains of 20–160 nm.