In this article, it is shown that a map $\xi$ : $\mathfrak{A} \rightarrow \mathfrak{A}$ (not necessarily linear) satisfies $\xi((A \circ B) \bullet C)=(\xi(A) \circ B) \bullet C+(A \circ \xi(B)) \bullet C+(A \circ B) \bullet \xi(C)$ holds for all $A, B, C \in \mathfrak{A}$ if and only if $\xi$ is an additive $\ast$-derivation where $\mathfrak{A}$ a unital $\ast$-algebra over the complex fields $\mathbb{C}$. As applications, we apply our main result to some special classes of unital $\ast$-algebras such as prime $\ast$-algebras, standard operator algebras, factor von Neumann algebras and von Neumann algebras with no central summands of type $I_1$.