Let \(G\) be a graph with adjacency matrix \(A(G)\), and let \(D(G)\) be the diagonal matrix of the degrees of \(G\). For any real \(\alpha\in[0,1]\), write \(A_\alpha(G)\) for the matrix \[A_\alpha(G)=\alpha D(G)+(1-\alpha)A(G).\] This paper presents some extremal results about the spectral radius \(\rho(A_\alpha(G))\) of \(A_\alpha(G)\) that generalize previous results about \(\rho(A_0(G))\) and \(\rho(A_{\frac{1}{2}}(G))\). In this paper, we give some results on graph perturbation for \(A_\alpha\)-matrix with \(\alpha\in [0,1)\). As applications, we characterize all extremal trees with the maximum \(A_\alpha\)-spectral radius in the set of all trees with prescribed degree sequence firstly. Furthermore, we characterize the unicyclic graphs that have the largest \(A_\alpha\)-spectral radius for a given unicycilc degree sequence.