Although the development of computer-aided algorithms for sleep staging is integrated into automatic detection of sleep disorders, most supervised deep learning-based models might suffer from insufficient labeled data. While the adoption of semi-supervised learning (SSL) can mitigate the issue, the SSL models are still limited to the lack of discriminative feature extraction for diverse obstructive sleep apnea (OSA) severity. This model deterioration might be exacerbated during the domain adaptation. Such exploration on the alleviation of domain-shift of SSL model between different OSA conditions has attracted more and more attentions from the clinic. In this work, a co-attention meta sleep staging network (CMS2-net) is proposed to simultaneously deal with two issues: the inter-class disparity problem and the intra-class selection problem. Within CMS2-net, a co-attention module and a triple-classifier are designed to explicitly refine the coarse feature representations by identifying the class boundary inconsistency. Moreover, the mutual information with meta contrastive variance is introduced to supervise the gradient stream from a multi-scale view. The performance of the proposed framework is demonstrated on both public and local datasets. Furthermore, our approach achieves the state-of-the-art SSL results on both datasets.