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A realization of the elliptic quantum algebra $U_{q,p}(\widehat{sl_2})$ forany given level $k$ is constructed in terms of three free boson fields andtheir accompanying twisted partners. It can be viewed as the ellipticdeformation of Wakimoto realization. Two screening currents are constructed;they commute or anti-commute with $U_{q,p}(\widehat{sl_2})$ modulo totalq-differences. The free fields realization for two types vertex operatorsnominated as the type $I$ and the type $II$ vertex operators are presented. Thetwisted version of the two types vertex operators are also obtained. They allplay crucial roles in calculating correlation functions.

On the Vertex Operators of the Elliptic Quantum Algebra $U_{q,p}(\widehat{sl_2})_{k}$}