Phosphorylation site prediction based on kinase-substrate interaction plays a vital role in understanding cellular signaling pathways and disease mechanisms. Computational methods for this task can be categorized into kinase-family-focused and individual kinase-targeted approaches. Individual kinase-targeted methods have gained prominence for their ability to explore a broader protein space and provide more precise target information for kinase inhibitors. However, most existing individual kinase-based approaches focus solely on sequence inputs, neglecting crucial structural information. To address this limitation, we introduce SAGEPhos (Structure-aware kinAse-substrate bio-coupled and bio-auGmented nEtwork for Phosphorylation site prediction), a novel framework that modifies the semantic space of main protein inputs using auxiliary inputs at two distinct modality levels. At the inter-modality level, SAGEPhos introduces a Bio-Coupled Modal Fusion method, distilling essential kinase sequence information to refine task-oriented local substrate feature space, creating a shared semantic space that captures crucial kinase-substrate interaction patterns. Within the substrate's intra-modality domain, it focuses on Bio-Augmented Fusion, emphasizing 2D local sequence information while selectively incorporating 3D spatial information from predicted structures to complement the sequence space. Moreover, to address the lack of structural information in current datasets, we contribute a new, refined phosphorylation site prediction dataset, which incorporates crucial structural elements and will serve as a new benchmark for the field. Experimental results demonstrate that SAGEPhos significantly outperforms baseline methods, notably achieving almost 10\% and 12\% improvements in prediction accuracy and AUC-ROC, respectively. We further demonstrate our algorithm's robustness and generalization through stable results across varied data partitions and significant improvements in zero-shot scenarios. These results underscore the effectiveness of constructing a larger and more precise protein space in advancing the state-of-the-art in phosphorylation site prediction. We release the SAGEPhos models and code at https://github.com/ZhangJJ26/SAGEPhos.