Debye shielding in an electron–ion plasma with regularized kappa distribution is examined. An unmagnetized collisionless plasma sheath with regularized kappa distributed electrons is investigated and the modified Bohm criterion is derived. It is found that the variation of the electrostatic potential depends significantly on the superthermal index κ and cutoff parameter α. If κ < 3/2, a plasma sheath with a regularized kappa distribution exists. Our present work may be useful in understanding plasma processing and plasma sheaths in related plasma regions (i.e., Earth’s inner magnetosphere).