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In this paper, we characterize the extremal digraphs with the maximal or minimal α-spectral radius among some digraph classes such as rose digraphs, generalized theta digraphs and tri-ring digraphs with given size m. These digraph classes are denoted by ℛ_m^k, Θ_k(m) and (m) respectively. The main results about spectral extremal digraph by Guo and Liu in and Li and Wang in are generalized to α-spectral graph theory. As a by-product of our main results, an open problem in is answered.arXiv:2105.03077v1 fatcat:tn6r4jmtkvdtjlow3vyqz3r5xy