Federated Learning (FL) is a distributed machine learning paradigm that enables multiple participants to collaboratively train high-performance models without transferring local data. This approach effectively protects data privacy and reduces communication costs. However, a critical challenge faced by FL is data heterogeneity across clients. Additionally, in practical FL applications, data scarcity on the client side is a common issue. While significant research has focused on addressing data heterogeneity, the simultaneous presence of data scarcity can lead to local model overfitting and drift, which in turn deteriorates the performance of the global model. To address both of these challenges, this paper introduces a novel federated learning framework called FedBE. FedBE mitigates local overfitting caused by data scarcity by combining local training samples with features from a buffer. Additionally, by using a synthetic and fixed ETF classifier, FedBE enables all clients, even in the presence of data heterogeneity, to learn unified and optimized feature representations, thereby enhancing the performance of the global model. Finally, to safeguard the privacy of the shared features in the buffer, FedBE incorporates differential privacy noise before storing client features. Experimental results show that FedBE provides an effective solution to the FL model under both heterogeneous and data-scarce conditions, while also mitigating privacy risks.