Effect modifier selection is important in the modeling of heterogeneous treatment effects. With data-driven selection of effect modifiers, the quantification of statistical uncertainty is complicated by post-selection inference. Since the selection is performed based on a single sample dataset, the naive inference procedures suffer from overfitting and usually produce an inflated type I error rate. We propose a Universal Post Selection Inference (UPoSI) procedure for the recently developed penalized G-estimator that performs doubly robust estimation of the causal effect of a time-varying exposure with a simultaneous data-adaptive selection of effect modifiers using longitudinal observational data. We perform a simulation study to compare the empirical false coverage rates produced by the proposed method with that obtained from the naive inference procedure based on sandwich variance estimates. We illustrate our method using the data arising from a study of hemodiafiltration.