The rapid spread of misinformation has made fact verification a critical necessity. LLM-based methods have become the mainstream approach for fact verification, but they still suffer from hallucinations. To mitigate hallucinations, researchers incorporate KG on LLM reasoning with a graph-based constrained decoding. However, these methods with constrained decoding suffer from error cascading due to the inherent knowledge gaps of the LLM, which cause it to select wrong branches during beam search in the constrained token space. To tackle error cascading, we think that the decoding process should be dynamically guided by step-level plausibility assessment. In light of this, we propose TrustFV (https://anonymous.4open.science/r/Trust_FV-6239), a fact verification framework that step-wise beam search in token-level constrained decoding with risk-averse pruning for trustworthy verification. Specifically, TrustFV integrates (1) token-level constrained decoding on a Knowledge Graph Tries (KG-Tries) to ground generation in retrieved evidence from KG, (2) an Uncertainty-aware Process Reward Model (UPRM) trained via Monte Carlo rollouts and ordinal regression to estimate both expected success and uncertainty per step, and (3) a step-wise beam search that actively prunes high-risk branches via the step-level signal of UPRM, producing faithful and plausible reasoning paths. Experiments show that TrustFV achieves state-of-the-art performance on FactKG and CWQ datasets.