Coreset, as a summary of training data, offers an efficient approach for reducing data processing and storage complexity during training. In the emerging vertical federated learning (VFL) setting, where scattered clients store different data features, it directly reduces communication complexity. In this work, we introduce coresets construction for regularized logistic regression both in centralized and VFL settings. Additionally, we improve the coreset size for regularized linear regression in the VFL setting. We also eliminate the dependency of the coreset size on a property of the data due to the VFL setting. The improvement in the coreset sizes is due to our novel coreset construction algorithms that capture the reduced model complexity due to the added regularization and its subsequent analysis. In experiments, we provide extensive empirical evaluation that backs our theoretical claims. We also report the performance of our coresets by comparing the models trained on the complete data and on the coreset.