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Accurate segmentation of solar filaments in H-alpha observations is critical for determining filament chirality, a key factor in the behavior of Coronal Mass Ejections (CMEs). However, existing methods often fail to capture fine-scale filament structures, particularly barbs, due to a limited ability to model long-range dependencies and spatial detail. We propose EdgeAttNet, a segmentation architecture built on a U-Net backbone by introducing a novel, learnable edge map derived directly from the input image. This edge map is incorporated into the model by linearly transforming the attention Key and Query matrices with the edge information, thereby guiding the self-attention mechanism at the network's bottleneck to more effectively capture filament boundaries and barbs. By explicitly integrating this structural prior into the attention computations, EdgeAttNet enhances spatial sensitivity and segmentation accuracy while reducing the number of trainable parameters. Trained end-to-end, EdgeAttNet outperforms U-Net and other U-Net-based transformer baselines on the MAGFILO dataset. It achieves higher segmentation accuracy and significantly better recognition of filament barbs, with faster inference performance suitable for practical deployment.