Brain age prediction serves as a powerful framework for assessing brain status and detecting deviations associated with neurodevelopmental and neurodegenerative disorders. However, most existing approaches emphasize whole-brain age prediction and therefore overlook the pronounced regional heterogeneity of brain maturation that is crucial for detecting localized atypical trajectories. To address this limitation, we propose a novel spherical surface-based brain age prediction network (SurfAge-Net) that leverages multiple morphological metrics to capture region-specific developmental patterns with enhanced robustness and clinical interpretability. SurfAge-Net establishes a new modeling paradigm by incorporating the connectomic principles of cortical organization: it explicitly models both intra- and inter-hemispheric dependencies through a spatial-channel mixing and a lateralization-aware attention mechanism, enabling the network to characterize the coordinate maturation pattern uniquely associated with each target region. Validated on three fetal and neonatal datasets, SurfAge-Net outperforms existing approaches (global MAE = 0.54, regional MAE = 0.45 in gestational/postmenstrual weeks) and demonstrates strong generalizability across external cohorts. Importantly, it provides spatially precise and biologically interpretable maps of cortical maturation, effectively identifying heterogeneous delays and regional-specific abnormalities in atypical developmental populations. These results established fine-grained brain age prediction as a promising paradigm for advancing neurodevelopmental research and supporting early clinical assessment.