Fact verification constitutes a pivotal application in the effort to combat the dissemination of disinformation, a concern that has recently garnered considerable attention. However, previous studies in the field of fact verification, particularly those focused on question-answering dialogue, have exhibited limitations, such as failing to fully exploit the potential of question structures and ignoring relevant label information during the verification process. In this paper, we introduce Label-Infused Iterative Information Interacting (LI4), a novel approach designed for the task of question-answering dialogue based fact verification. LI4 consists of two meticulously designed components, namely the Iterative Information Refining and Filtering Module (IIRF) and the Fact Label Embedding Module (FLEM). The IIRF uses the Interactive Gating Mechanism to iteratively filter out the noise of question and evidence, concurrently refining the claim information. The FLEM is conceived to strengthen the understanding ability of the model towards labels by injecting label knowledge. We evaluate the performance of the proposed LI4 on HEALTHVER, FAVIQ, and COLLOQUIAL. The experimental results confirm that our LI4 model attains remarkable progress, manifesting as a new state-of-the-art performance.