In edge computing, energy-limited distributed edge clients present challenges such as heterogeneity, high energy consumption, and security risks. Traditional blockchain-based federated learning (BFL) struggles to address all three of these challenges simultaneously. This article proposes a Graph-Partitioning Multi-Granularity Federated Learning method on a consortium blockchain, namely GP-MGFL. To reduce the overall communication overhead, we adopt a balanced graph partitioning algorithm while introducing observer and consensus nodes. This method groups clients to minimize high-cost communications and focuses on the guidance effect within each group, thereby ensuring effective guidance with reduced overhead. To fully leverage heterogeneity, we introduce a cross-granularity guidance mechanism. This mechanism involves fine-granularity models guiding coarse-granularity models to enhance the accuracy of the latter models. We also introduce a credit model to adjust the contribution of models to the global model dynamically and to dynamically select leaders responsible for model aggregation. Finally, we implement a prototype system on real physical hardware and compare it with several baselines. Experimental results show that the accuracy of the GP-MGFL algorithm is 5.6% higher than that of ordinary BFL algorithms. In addition, compared to other grouping methods, such as greedy grouping, the accuracy of the proposed method improves by about 1.5%. In scenarios with malicious clients, the maximum accuracy improvement reaches 11.1%. We also analyze and summarize the impact of grouping and the number of clients on the model, as well as the impact of this method on the inherent security of the blockchain itself.