Summary: \((S,*)\) is a semigroup \(S\) equipped with a unary operation ``\(*\)''. This work is devoted to a class of unary semigroups, namely \(E\)-inversive \(*\)-semigroups. A unary semigroup \((S,*)\) is called an \(E\)-inversive \(*\)-semigroup if the following identities hold: \(x^*xx^*=x^*\), \((x^*)^*=xx^*x\), \((xy)^*=y^*x^*\). In this paper, \(E\)-inversive \(*\)-semigroups are characterized by several methods. Furthermore, congruences on these semigroups are also studied.