Ion‐acoustic supersolitons are investigated in an unmagnetized two‐temperature electron plasma comprising cold fluid ions, hot nonextensive electrons, and cool Maxwellian electrons by using the Sagdeev pseudopotential technique. Existence domain of positive polarity supersolitons in terms of Mach number is computed, which is found to exist for Mach numbers beyond the existence of positive double layers. The domain of existence of supersolitons diminishes with the decrease of the nonextensive parameter (q). The amplitude and width of the supersolitons are dependent on the cool‐to‐hot electron temperature ratio (τ), cool electron density (f), and nonextensive parameter (q). The increase of cool electron density increases the amplitude of the supersolitons. For fixed values of f, q, and Mach numbers, the decrease of τ exhibits more distinct wiggles in the electric fields of supersolitons. The present work may be helpful for further study of supersolitons in the auroral plasma.