Additivity of maps preserving Jordan $\eta_{\ast}$-products on‎ ‎$C^{*}$-algebras

‎Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^{*}$-algebras such‎ ‎that $\mathcal{B}$ is prime‎. ‎In this paper‎, ‎we investigate the‎ ‎additivity of maps $\Phi$ from $\mathcal{A}$ onto $\mathcal{B}$ that‎ ‎are bijective‎, ‎unital and < that > satisfy $\Phi(AP+\eta PA^{*})=\Phi(A)\Phi(P)+\eta \Phi(P)\Phi(A)^{*},$‎ ‎for all $A\in\mathcal{A}$ and $P\in\{P_{1},I_{\mathcal{A}}-P_{1}\}$‎ ‎where $P_{1}$ is a nontrivial projection in $\mathcal{A}$‎. ‎If‎ ‎$\eta$ is a non-zero complex number such that $|\eta|\neq1$‎, ‎then‎ ‎$\Phi$ is additive‎. ‎Moreover‎, ‎if $\eta$ is rational < , > then $\Phi$ is‎ ‎$\ast$-additive.