Spatio-temporal　prediction　is　vital　for　enabling　intelligent　urban　services.　However,　due　to　newly　deployed　infrastructure,　developing　cities　often　suffer　from　data　scarcity,　which　significantly　limits　the　applicability　of　deep　learning　models　that　rely　on　large　volumes　of　historical　data.　Moreover,　most　existing　methods　focus　solely　on　pairwise　spatial　interactions,　overlooking　complex　high-order　spatial　dependencies　that　are　crucial　for　accurate　prediction.　To　address　these　challenges,　we　propose　D2MHyper,　a　cross-city　spatio-temporal　prediction　framework　that　integrates　high-order　spatial　information　through　a　Dynamic　Multi-scale　Hypergraph　neural　network　enhanced　by　Domain　adversarial　training.　Specifically,　we　design　a　shared-private　representation　learning　strategy　that　captures　both　city-invariant　and　city-specific　spatial　features　through　inter-city　shared　and　intra-city　private　hypergraphs.　To　effectively　model　complex　dependencies,　we　develop　a　dynamic　multi-scale　hypergraph　generation　module　based　on　learnable　incidence　matrices,　which　captures　implicit　time-varying　high-order　interactions　at　multiple　granularities.　To　enhance　generalization　to　data-scarce　target　cities,　a　cross-city　knowledge　transfer　module　is　introduced　to　transfer　global　information　from　source　cities.　Furthermore,　a　domain　adversarial　training　strategy　is　incorporated　to　enforce　the　disentanglement　of　shared　and　private　representations.　Extensive　experiments　on　four　real-world　benchmark　datasets　consistently　validate　the　effectiveness　of　D2MHyper,　which　outperforms　state-of-the-art　methods　in　cross-city　prediction　under　data　scarcity　scenarios.