Recent studies in medical question answering (Medical QA) have actively explored the integration of large language models (LLMs) with biomedical knowledge graphs (KGs) to improve factual accuracy. However, most existing approaches still rely on traversing the entire KG or performing large-scale retrieval, which introduces substantial noise and leads to unstable multi-hop reasoning. We argue that the core challenge lies not in expanding access to knowledge, but in identifying and reasoning over the appropriate subset of evidence for each query. ReGraM is a region-first knowledge graph reasoning framework that addresses this challenge by constructing a query-aligned subgraph and performing stepwise reasoning constrained to this localized region under multiple evidence aware modes. By focusing inference on only the most relevant portion of the KG, ReGraM departs from the assumption that all relations are equally useful an assumption that rarely holds in domain-specific medical settings. Experiments on seven medical QA benchmarks demonstrate that ReGraM consistently outperforms a strong baseline (KGARevion), achieving an 8.04% absolute accuracy gain on MCQ, a 4.50% gain on SAQ, and a 42.9% reduction in hallucination rate. Ablation and qualitative analyses further show that aligning region construction with hop-wise reasoning is the primary driver of these improvements. Overall, our results highlight region-first KG reasoning as an effective paradigm for improving factual accuracy and consistency in medical QA.