Deep learning-based Automatic Modulation Recognition (AMR) model has made significant progress with the support of large-scale labeled data. However, when developing new models or performing hyperparameter tuning, the time and energy consumption associated with repeated training using massive amounts of data are often unbearable. To address the above challenges, we propose \emph{FoQuS}, which approximates the effect of full training by selecting a coreset from the original dataset, thereby significantly reducing training overhead. Specifically, \emph{FoQuS} records the prediction trajectory of each sample during full-dataset training and constructs three importance metrics based on training dynamics. Experiments show that \emph{FoQuS} can maintain high recognition accuracy and good cross-architecture generalization on multiple AMR datasets using only 1\%-30\% of the original data.