Summary: In this paper, we study the generalizations of Euler numbers and polynomials by using the \(q\)-extension with \(p\)-adic integral on \(\mathbb{Z}_p\). We call these: the generalized \(q\)-\(\omega\)-Euler numbers \(E^{(\alpha)}_{n,q,\omega}(a)\) and polynomials \(E^{(\alpha)}_{n,q,\omega}(x;a)\). We investigate some elementary properties and relations for \(E^{(\alpha)}_{n,q,\omega}(a)\) and \(E^{(\alpha)}_{n,q,\omega}(x;a)\).