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The main purpose of this article is to introduce and investigate the subcategory $mathcal{H}_{Sigma}(n,beta;phi)$ of bi-univalent functions in the open unit disk $mathbb{U}$ related to subordination. Moreover,  estimates on coefficient $|a_n|$ for functions belong to this subcategory are given applying different technique. In addition,  smaller upper bound and more accurate estimation than the previous outcomes are obtained.