Distributed learning is widely regarded as an effective solution for edge computing in the current data-intensive era. By eliminating heavy data transfers inherent to centralized machine learning, it enables participants to train models locally without aggregating raw data on a cloud server. However, data at distributed clients is often missing or tampered with, which leads to inaccurate gradients during training and opens the door to falsified or manipulated updates. To address the issue that heterogeneous data quality among clients in distributed learning may degrade the performance of the global model, this paper proposes an admission and continuous verification mechanism for federated learning based on Proof of Data Possession (PDP). In this mechanism, the proof of data possession serves as a prerequisite for client participation. Each client must demonstrate the integrity and authenticity of its designated dataset, thereby filtering out clients with incorrect or unreliable data. Furthermore, a continuous random sampling verification strategy is innovatively introduced during the federated training process, where clients that repeatedly fail the proof are eliminated. In practical deployment, considering the differences in computational capabilities among devices, they are categorized into high-capacity and low-capacity devices. A hierarchical PDP mechanism is designed accordingly: high-capacity devices perform integrity verification using BLS signatures, while low-capacity devices adopt sampling-based verification. The scheme further integrates aggregated proofs to reduce time overhead and improve overall efficiency.