Conversational question answering (ConvQA) over heterogeneous sources leverages information from heterogeneous sources to enhance answer coverage, thereby improving the performance of ConvQA systems. Current mainstream methods rely on neural Seq2Seq models focusing on the complete conversation history. These models extract question entities and relation phrases implicit in the conversation history through sequence generation. However, numerous errors occur in extracting question entities because the conversation history contains irrelevant noise, and the sequence generation approach may lead to inaccuracies. To address this problem, we propose a model that incorporates a syntax tree and a graph neural network for ConvQA over heterogeneous sources. The model constructs a syntax tree by syntactically analyzing the user’s question and conversation history. It then learns node representations and predicts node scores of the word nodes in the tree. This is based on the node’s entity information and its relevance to the current question within the neighborhood. A graph neural network that includes entity-level attention is used to complete the extraction of the question entities. Experiments on the ConvMix and ConvQuestions datasets verify the overall performance improvement and validate the effectiveness of the proposed model.