Accommodating edge networks between IoT devices and the cloud server in Hierarchical Federated Learning (HFL) enhances communication efficiency without compromising data privacy. However, devices connected to the same edge often share geographic or contextual similarities, leading to varying edge-level data heterogeneity with different subsets of labels per edge, on top of device-level heterogeneity. This hierarchical non-Independent and Identically Distributed (non-IID) nature, which implies that each edge has its own optimization goal, has been overlooked in HFL research. Therefore, existing edge-accommodated HFL demonstrates inconsistent performance across edges in various hierarchical non-IID scenarios. To ensure robust performance with diverse edge-level non-IID data, we propose a Personalized Hierarchical Edge-enabled Federated Learning (PHE-FL), which personalizes each edge model to perform well on the unique class distributions specific to each edge. We evaluated PHE-FL across 4 scenarios with varying levels of edge-level non-IIDness, with extreme IoT device level non-IIDness. To accurately assess the effectiveness of our personalization approach, we deployed test sets on each edge server instead of the cloud server, and used both balanced and imbalanced test sets. Extensive experiments show that PHE-FL achieves up to 83 percent higher accuracy compared to existing federated learning approaches that incorporate edge networks, given the same number of training rounds. Moreover, PHE-FL exhibits improved stability, as evidenced by reduced accuracy fluctuations relative to the state-of-the-art FedAvg with two-level (edge and cloud) aggregation.