Fake news detection is a significant challenge in the digital age, which has become increasingly important with the proliferation of social media and online communication networks. Graph Neural Networks (GNN)-based methods have shown high potential in analyzing graph-structured data for this problem. However, a major limitation in conventional GNN architectures is their inability to effectively utilize information from neighbors beyond the network's layer depth, which can reduce the model's accuracy and effectiveness. In this paper, we propose a novel model called Neighborhood-Order Learning Graph Attention Network (NOL-GAT) for fake news detection. This model allows each node in each layer to independently learn its optimal neighborhood order. By doing so, the model can purposefully and efficiently extract critical information from distant neighbors. The NOL-GAT architecture consists of two main components: a Hop Network that determines the optimal neighborhood order and an Embedding Network that updates node embeddings using these optimal neighborhoods. To evaluate the model's performance, experiments are conducted on various fake news datasets. Results demonstrate that NOL-GAT significantly outperforms baseline models in metrics such as accuracy and F1-score, particularly in scenarios with limited labeled data. Features such as mitigating the over-squashing problem, improving information flow, and reducing computational complexity further highlight the advantages of the proposed model.