The news stream on social media has become the primary source for instant insights into real-world topics. However, the rapid spread of fake news poses a significant challenge that needs to be strictly addressed. Existing fake news detection methods analyze individual news articles in a temporally sequenced news stream but often overlook the topic-based correlations. Consequently, they inefficiently detect incoming fake news related to similar topics with prior fake likelihoods. To enhance the detection efficiency of incoming fake news in news streams, this study introduces an efficient Topic-based Correlation Framework (TCF) consisting of two innovative components: the dynamic correlation mapping module and the transfer correlation learning module. The dynamic correlation mapping module utilizes an incremental clustering approach to establish mapping relationships between news articles and topics. It automatically classifies the input news passages into familiar and unfamiliar topic domains. In addition, the transfer correlation learning module employs a domain adaptation network to detect incoming fake news across familiar and unfamiliar topic domains. By leveraging this approach, our proposed framework demonstrates superior performance compared to existing state-of-the-art methods in detecting incoming fake news in news streams.