Hyperspectral image (HSI) classification is an emerging need in remote sensing applications. Extraction of spatial and spectral cues, and their relevance, are crucial for the classification of HSI. Notable research has progressed to address challenges in HSI classifications, including pixel boundary correspondences, spectral band similarities, and high-dimensional issues. Recent methods, specifically SclusterFormer, have primarily focused on these issues and have achieved significant improvements in HSI classification. It effectively enables spectral and spatial information using cluster-based attention and processes features independently and combines them through a simple additive fusion strategy, which limits its ability to model cross-dimensional dependencies. To address these limitations, a Cross-Dimensional Spectral–Spatial Fusion Framework (CDSSF) is proposed. The proposed method introduces an adaptive attention-based fusion mechanism that dynamically integrates spectral and spatial features, enabling effective interaction across dimensions. This enhances feature discrimination, improves robustness to spectral variability, and leads to superior classification performance compared to the baseline model.