Accurate segmentation of wrist bones from conventional radiographs remains a significant challenge due to severe anatomical overlap and blurred bone boundaries, particularly in patients with rheumatoid arthritis. To address these issues, we propose AP-DPM, a novel Dual-Path Prior-constrained Merging model with adversarial anatomical priors. AP-DPM employs a dual-path architecture to separately predict complete bone masks and overlapping regions, which are subsequently integrated through a residual merging network. To enhance anatomical plausibility, we incorporate an adversarial prior guided by a pre-trained discriminator. Extensive experiments on the publicly available RAM-W600 dataset demonstrate that AP-DPM outperforms state-of-the-art methods across seven quantitative metrics, achieving superior performance particularly in diagnostically critical overlapping regions. Ablation studies further validate that both the dual-path structure for enhanced focusing on overlap regions and the adversarial anatomical prior contribute significantly to performance gains, enhancing local boundary sensitivity and global structural consistency. These results highlight the potential of AP-DPM to improve automated radiographic assessment of rheumatoid arthritis progression.