We develop an interquantile shrinkage estimation to explore the underlying commonality structure of regression coefficients across different quantile levels for longitudinal data in a data-driven manner. It provides a more insightful view between the response and covariates and enhances estimation efficiency and model interpretability. We propose a fused penalized generalized estimation equation (GEE) estimator under a non-crossing constraint to automatically promote the constancy of estimates across neighboring quantiles. The GEE estimator accommodates the within-subject correlation for longitudinal data to improve estimation efficiency. A nested alternating direction method of multiplier (ADMM) algorithm is developed to minimize the regularized objective function. The asymptotic properties of the penalized estimators are also well established. In addition, when irrelevant predictors exist in high dimensions, we also develop a doubly penalized GEE estimator to select important variables and identify the interquantile commonality simultaneously. Numerical studies demonstrate that the proposed methods enjoy higher estimation efficiency than several existing methods. A longitudinal wage empirical data set is analyzed to further illustrate our methodologies.