Let G be a mixed graph and alpha is an element of[0,1]. Let D(G) and A(G) be the diagonal matrix of vertex degrees and the mixed adjacency matrix of G, respectively. The alpha -mixed adjacency matrix of G is the matrix A(alpha)(G)=D-alpha(G)+(1-alpha)A(G).We study some properties of A(alpha)(G) associated with some type of mixed graphs, namely quasi-bipartite and pre-bipartite mixed graphs. A spectral characterization for pre-bipartite and some class of quasi-bipartite mixed graphs is given. For a mixed graph G we exploit the problem of finding the smallest alpha for which A(alpha)(G) is positive semi-definite. This problem was proposed by Nikiforov in the context of undirected graphs. It is proven here that, for a mixed graph this number is not greater than 12 and that a connected mixed graph G with n >= 2 is quasi-bipartite if and only if this number is exactly 12. The spread of the alpha -mixed adjacency matrix is the difference among the largest and the smallest alpha -mixed adjacency eigenvalue. Upper and lower bounds for the spread of the alpha - mixed adjacency matrix are obtained. The alpha -mixed Estrada index of G is the sum of the exponentials of the eigenvalues of A(alpha)(G). In this paper, bounds for the eigenvalues of A(alpha)(G) are established and, using these bounds some sharp bounds on the mixed Estrada index of A(alpha)(G) are presented.