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Quantile estimates are generally interpreted in association with the return period concept in practical engineering. To do so with the peaks-over-threshold (POT) approach, combined Poisson-generalized Pareto distributions (referred to as PD-GPD model) must be considered. In this article, we evaluate the incorporation of non-stationarity in the generalized Pareto distribution (GPD) and the Poisson distribution (PD) using, respectively, the smoothing-based B-spline functions and the logarithmic link function. Two models are proposed, a stationary PD combined to a non-stationary GPD (referred to as PD0-GPD1) and a combined non-stationary PD and GPD (referred to as PD1-GPD1). The teleconnections between hydro-climatological variables and a number of large-scale climate patterns allow using these climate indices as covariates in the development of non-stationary extreme value models. The case study is made with daily precipitation amount time series from southeastern Canada and two climatic covariates, the Arctic Oscillation (AO) and the Pacific North American (PNA) indices. A comparison of PD0-GPD1 and PD1-GPD1 models showed that the incorporation of non-stationarity in both POT models instead of solely in the GPD has an effect on the estimated quantiles. The use of the B-spline function as link function between the GPD parameters and the considered climatic covariates provided flexible non-stationary PD-GPD models. Indeed, linear and nonlinear conditional quantiles are observed at various stations in the case study, opening an interesting perspective for further research on the physical mechanism behind these simple and complex interactions.