Summary: In this paper, by using the techniques of the \(q\)-exponential generating series, we extend a well-known two-parameter identity for the Appell polynomials to the \(q\)-Appell polynomials of type I and II. More precisely, we obtain two different \(q\)-analogues of such an identity. Then, we specialize these identities for some \(q\)-polynomials arising in combinatorics, in \(q\)-calculus or in the theory of orthogonal polynomials. In particular, we consider the generalized \(q\)-Bernoulli and \(q\)-Euler polynomials and then we deduce some further identities involving the Bernoulli and Euler numbers. In this way, as a byproduct, we derive the symmetric Carlitz identity for the Bernoulli numbers. Finally, we find a (non-symmetric) \(q\)-analogue of Carlitz's identity involving the \(q\)-Bernoulli numbers of type I and II.