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Federated learning (FL) has emerged as a new paradigm of machine learning (ML) with the goal of collaborative learning on the vast pool of private data available across distributed edge devices. The focus of most existing works in FL systems has been on addressing the challenges of computation and communication heterogeneity inherent in training with edge devices. However, the crucial impact of I/O and the role of limited on-device storage has not been explored fully in FL context. Without policies to exploit the on-device storage for placement of client data samples, and schedule clients based on I/O benefits, FL training can lead to inefficiencies, such as increased training time and impacted accuracy convergence. In this paper, we propose FedCaSe, a framework for efficiently caching client samples in-situ on limited on-device storage and scheduling client participation. FedCaSe boosts the I/O performance by exploiting a unique characteristic---the experience, i.e., relative impact on overall performance, of data samples and clients. FedCaSe utilizes this information in adaptive caching policies for sample placement inside the limited memory of edge clients. The framework also exploits the experience information to orchestrate the future selection of clients. Our experiments with representative workloads and policies show that compared to the state of the art, FedCaSe improves the training time by 2.06x for accuracy convergence at the scale of thousands of clients.