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Object pose estimation is a fundamental task in 3D vision with applications in robotics, AR/VR, and scene understanding. We address the challenge of category-level 9-DoF pose estimation (6D pose + 3Dsize) from RGB-D input, without relying on CAD models during inference. Existing depth-only methods achieve strong results but ignore semantic cues from RGB, while many RGB-D fusion models underperform due to suboptimal cross-modal fusion that fails to align semantic RGB cues with 3D geometric representations. We propose DeMo-Pose, a hybrid architecture that fuses monocular semantic features with depth-based graph convolutional representations via a novel multimodal fusion strategy. To further improve geometric reasoning, we introduce a novel Mesh-Point Loss (MPL) that leverages mesh structure during training without adding inference overhead. Our approach achieves real-time inference and significantly improves over state-of-the-art methods across object categories, outperforming the strong GPV-Pose baseline by 3.2\% on 3D IoU and 11.1\% on pose accuracy on the REAL275 benchmark. The results highlight the effectiveness of depth-RGB fusion and geometry-aware learning, enabling robust category-level 3D pose estimation for real-world applications.