Abstract: The green electricity-hydrogen-ammonia coupling system has gained significant attention for its role in the transition to a zero-carbon economy, with diverse applications promoting sustainable development. However, its scheduling is challenged by multiple uncertainties. Due to the diversity of data and the complexity of the environment, uncertainties often exhibit multimodal characteristics, but this is often overlooked, resulting in conservative scheduling outcomes. To this end, this paper proposes an adaptive distributionally robust scheduling framework to manage uncertainties of renewable energy and demands within this coupling system. We adopt clustering algorithms to extract multi-modality information from the uncertainty data and establish a mixture Wasserstein ambiguity set to accurately represent uncertainty distributions. Finally, we equivalently reformulate this distributionally robust scheduling problem into a mixed-integer linear programming problem using affine decision rules, while ensuring non-anticipativity and adaptability. Case studies demonstrate that, in in-sample tests, our method outperforms Wasserstein distributionally robust optimization and robust optimization by 3.48% and 7.54%, respectively. In out-of-sample tests, our method achieves improvements of 2.75% and 6.54% over Wasserstein distributionally robust optimization and robust optimization, respectively.