Let $A(G)$ be the adjacency matrix and $D(G)$ be the diagonal matrix of the vertex degrees of a simple connected graph $G$. Nikiforov defined the matrix $A_α(G)$ of the convex combinations of $D(G)$ and $A(G)$ as $A_α(G)=αD(G)+(1-α)A(G)$, for $0\leq α\leq 1$. If $ ρ_{1}\geq ρ_{2}\geq \dots \geq ρ_{n}$ are the eigenvalues of $A_α(G)$ (which we call $α$-adjacency eigenvalues of $G$), the $ α$-adjacency energy of $G$ is defined as $E^{A_α}(G)=\sum_{i=1}^{n}\left|ρ_i-\frac{2αm}{n}\right|$, where $n$ is the order and $m$ is the size of $G$. We obtain the upper and lower bounds for $E^{A_α}(G) $ in terms of order $n$, size $m$ and Zagreb index $Zg(G)$ associated to the structure of $G$. Further, we characterize the extremal graphs attaining these bounds.