Schema, a form of structured knowledge that promotes transfer learning, is attracting growing attention in both neuroscience and artificial intelligence (AI). Current schema research in neural computation is largely constrained to a single behavioral paradigm and relies heavily on recurrent neural networks (RNNs) which lack the neural plausibility and biological interpretability. To address these limitations, this work first constructs a generalized behavioral paradigm framework for schema learning and introduces three novel cognitive tasks, thus supporting a comprehensive schema exploration. Second, we propose a new model using recurrent spiking neural networks with hierarchical intrinsic excitability modulation (HM-RSNNs). The top level of the model selects excitability properties for task-specific demands, while the bottom level fine-tunes these properties for intra-task problems. Finally, extensive visualization analyses of HM-RSNNs are conducted to showcase their computational advantages, track the intrinsic excitability evolution during schema learning, and examine neural coordination differences across tasks. Biologically inspired lesion studies further uncover task-specific distributions of intrinsic excitability within schemas. Experimental results show that HM-RSNNs significantly outperform RSNN baselines across all tasks and exceed RNNs in three novel cognitive tasks. Additionally, HM-RSNNs offer deeper insights into neural dynamics underlying schema learning.