Let \(\mathcal {R}\) be a \(\{2, n-1\}\) -torsion free unital prime \(*\) -ring containing a nontrivial symmetric idempotent. For any \(x_1, x_2,\ldots , x_n\in \mathcal {R},\) define \(q_1(x_1)=x_1,\) \(q_2(x_1, x_2)=[x_1, x_2]_{*}=x_1x_2-x_2x_1^{*}\) and \(q_n(x_1, x_2,\ldots , x_n)=[q_{n-1}(x_1, x_2,\ldots , x_{n-1}), x_n]_{*}\) for all integers \(n\ge 2.\) In this paper, we establish the relationship between multiplicative skew Lie-type derivations and additive \(*\) -derivations on prime \(*\) -rings, that is, we prove that a map \(\delta :\mathcal {R}\rightarrow \mathcal {R}\) satisfies \(\begin{aligned} \delta (q_n(x_1, x_2,\ldots , x_n))=\sum \limits _{i=1}^{n}q_n(x_1, x_2,\ldots , x_{i-1}, \delta (x_i), x_{i+1},\ldots , x_n) \end{aligned}\) for all \(x_1, x_2,\ldots , x_n\in \mathcal {R}\) if and only if it is an additive \(*\) -derivation. As an application, multiplicative skew Lie-type derivations on factor von Neumann algebras have been characterized.