Misinformation spreading over the Internet poses a significant threat to both societies and individuals, necessitating robust and scalable fact-checking that relies on retrieving accurate and trustworthy evidence. Previous methods rely on semantic and social-contextual patterns learned from training data, which limits their generalization to new data distributions. Recently, Retrieval Augmented Generation (RAG) based methods have been proposed to utilize the reasoning capability of LLMs with retrieved grounding evidence documents. However, these methods largely rely on textual similarity for evidence retrieval and struggle to retrieve evidence that captures multi-hop semantic relations within rich document contents. These limitations lead to overlooking subtle factual correlations between the evidence and the claims to be fact-checked during evidence retrieval, thus causing inaccurate veracity predictions.