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Despite recent progress in improving the performance of misinformation detection systems, classifying misinformation in an unseen domain remains an elusive challenge. To address this issue, a common approach is to introduce a domain critic and encourage domain-invariant input features. However, early misinformation often demonstrates both conditional and label shifts against existing misinformation data (e.g., class imbalance in COVID-19 datasets), rendering such methods less effective for detecting early misinformation. In this paper, we propose contrastive adaptation network for early misinformation detection (CANMD). Specifically, we leverage pseudo labeling to generate high-confidence target examples for joint training with source data. We additionally design a label correction component to estimate and correct the label shifts (i.e., class priors) between the source and target domains. Moreover, a contrastive adaptation loss is integrated in the objective function to reduce the intra-class discrepancy and enlarge the inter-class discrepancy. As such, the adapted model learns corrected class priors and an invariant conditional distribution across both domains for improved estimation of the target data distribution. To demonstrate the effectiveness of the proposed CANMD, we study the case of COVID-19 early misinformation detection and perform extensive experiments using multiple real-world datasets. The results suggest that CANMD can effectively adapt misinformation detection systems to the unseen COVID-19 target domain with significant improvements compared to the state-of-the-art baselines.