Multi-source multi-hop question answering (QA) represents a challenging task in natural language processing due to the need for dynamic integration of heterogeneous knowledge sources and multi-step reasoning. Existing methods often suffer from cascading errors, insufficient handling of knowledge conflicts, and computational inefficiency. In this paper, we propose Adaptive Multi-source Knowledge-Oriented Reasoning (AMKOR), a generative framework that leverages large language models (LLMs) to dynamically fuse parametric and retrieved knowledge while exploring reasoning trajectories using probabilistic beam reasoning. AMKOR is further enhanced by a multi-granular learning strategy, optimizing both local reasoning steps and global answer accuracy. Experiments conducted on four widely-used multi-hop QA datasets, including HotpotQA and MuSiQue, demonstrate that AMKOR achieves state-of-the-art performance, significantly outperforming baseline methods on both reasoning accuracy and robustness. Additional analyses confirm its scalability, adaptability to noisy knowledge, and superior ability to handle complex multi-hop tasks. This work establishes a new benchmark for multi-source multi-hop QA by effectively combining reasoning quality and efficiency.