Let R be a *-ring and n >= 1 be an integer. The objective of this paper is to introduce the notion of n-skew centralizing maps on *-rings, and investigate the impact of these maps. In particular, we describe the structure of prime rings with involution '*' such that (*)[x, d(x)](n) is an element of Z(R) for all x is an element of R (for n = 1, 2), where d : R -> R is a nonzero derivation of R. Among other related results, we also provide two examples to prove that the assumed restrictions on our main results are not superfluous.