Cross-silo federated learning (FL) frequently faces challenges with non-independent and identically distributed (non-IID) data across clients, leading to a decline in the accuracy of FL model training. Although personalized FL (PFL) methods have been proposed to address this issue, they generally focus on specific levels of statistical heterogeneity. Furthermore, privacy constraints frequently obscure data heterogeneity, making it difficult to select a targeted PFL. To overcome this issue, we propose FedASH, a personalized cross-silo FL framework that adapts to diverse degrees of heterogeneity with two key components. The first component is adaptive proximal directed relationships, which dynamically adjust each client’s reliance on private and shared models, effectively adapting to different levels of data heterogeneity. The second component is client weight evaluation based on gradient, which assesses corresponding weights based on the similarity between the client and server update directions, achieving more effective aggregation. We conduct experiments on multiple datasets, including Fashion-MNIST, CIFAR-10, CIFAR-100, and a Parkinson’s disease dataset, and benchmark FedASH against several other FL methods. Experimental results confirm that our framework consistently achieves superior accuracy across diverse datasets.