Summary: Least-squares regularized learning algorithms for regression were well-studied in the literature when the sampling process is independent and the regularization term is the square of the norm in a reproducing kernel Hilbert space (RKHS). Some analysis has also been done for dependent sampling processes or regularizers being the qth power of the function norm (\(q\)-penalty) with \(0<q\leq 2\). The purpose of this article is to conduct error analysis of the least-squares regularized regression algorithm when the sampling sequence is weakly dependent satisfying an exponentially decaying \(\alpha\)-mixing condition and when the regularizer takes the \(q\)-penalty with \(0<q\leq 2\). We use a covering number argument and derive learning rates in terms of the \(\alpha\)-mixing decay, an approximation condition and the capacity of balls of the RKHS.