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Covariate-dependent processes have been widely used in Bayesian nonparametric statistics thanks to their flexibility to incorporate covariate information and correlation among process realizations. Unlike most of the existing work that focuses on extensions of exchangeable species sampling processes such as Dirichlet process, a new class of covariate-dependent nonexchangeable priors is proposed by considering the generalization of an nonexchangeable sequence, namely the Beta-GOS model. The proposed prior has an equivalent formulation under a continuous kernel mixture. It also has a latent variable representation that leads to a natural nonexchangeable parallel with the classical dependent Dirichlet process formulation. This prior is further applied in regression and autoregressive models and it is shown that its posterior sampling algorithm enjoys the same computational complexity with that of the Beta-GOS. The excellent numerical performance of the method is demonstrated via simulation and two real data examples. [ABSTRACT FROM AUTHOR]