This paper's major goal is to describe the structure of the $*$-prime ring, with the help of three different derivations $\alpha$, $\beta$ and $\gamma$ such that $\alpha([s_1,s_1^*])+[\beta(s_1),\beta(s_1^*)]+[\gamma(s_1), s_1^*]\in \Za(\chi)$ for all $s_1\in \chi$. Further, some more related results have also been discussed. As applications, classical theorems due to Bell-Daif \cite{BD1995} and Herstein \cite{INH2} are deduced.