Hyper-partisan misinformation has become a major public concern. In order to examine what type of misinformation label can mitigate hyper-partisan misinformation sharing on social media, we conducted a 4 (label type: algorithm, community, third-party fact-checker, and no label) X 2 (post ideology: liberal vs. conservative) between-subjects online experiment (N = 1,677) in the context of COVID-19 health information. The results suggest that for liberal users, all labels reduced the perceived accuracy and believability of fake posts regardless of the posts' ideology. In contrast, for conservative users, the efficacy of the labels depended on whether the posts were ideologically consistent: algorithmic labels were more effective in reducing the perceived accuracy and believability of fake conservative posts compared to community labels, whereas all labels were effective in reducing their belief in liberal posts. Our results shed light on the differing effects of various misinformation labels dependent on people's political ideology.