Pair of generalized skew derivations with power values on lie ideals in prime rings

In this article, we investigate the behavior of generalized skew derivations on prime rings. Let be a prime ring of characteristic not equal to 2 with right Martindale quotient ring and be a non-central Lie ideal of . Denote by the extended centroid of . We show that if and are generalized skew derivations of satisfying for all and some fixed , then necessarily and , unless satisfies the standard identity . This result extends the study of structural constraints imposed by derivation-like mappings on prime rings and highlights the exceptional role of the identity .