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Accurate identification of protein-nucleotide binding sites is fundamental to deciphering molecular mechanisms and accelerating drug discovery. However, current computational methods often struggle with suboptimal performance due to inadequate feature representation and rigid fusion mechanisms, which hinder the effective exploitation of cross-task information synergy. To bridge this gap, we propose MTGA-MGE, a framework that integrates a Multi-Task Genetic Algorithm with Multi-Granularity Encoding to enhance binding site prediction. Specifically, we develop a Multi-Granularity Encoding (MGE) network that synergizes multi-scale convolutions and self-attention mechanisms to distill discriminative signals from high-dimensional, redundant biological data. To overcome the constraints of static fusion, a genetic algorithm is employed to adaptively evolve task-specific fusion strategies, thereby effectively improving model generalization. Furthermore, to catalyze collaborative learning, we introduce an External-Neighborhood Mechanism (ENM) that leverages biological similarities to facilitate targeted information exchange across tasks. Extensive evaluations on fifteen nucleotide datasets demonstrate that MTGA-MGE not only establishes a new state-of-the-art in data-abundant, high-resource scenarios but also maintains a robust competitive edge in rare, low-resource regimes, presenting a highly adaptive scheme for decoding complex protein-ligand interactions in the post-genomic era.