Federated learning (FL) enables collaborative model training across distributed edge devices while preserving data privacy, but faces fundamental challenges from statistical het erogeneity, communication bottlenecks, and diverse device capabilities in wireless networks. Existing personalized FL approaches either maintain uniform model architectures or apply predefined compression strategies, failing to exploit client-specific adaptation for enhanced personalization and communication efficiency. We propose FedPAP, a personalized federated learning framework that enables each client to independently discover optimal sparse model structures tailored to local data characteristics. The core innovation is the APSF method, which efficiently determines client-specific pruning ratios through surrogate-based optimization, integrated with a personalized masked weight aggregation strategy that facilitates selective knowledge transfer among het erogeneously pruned models. We establish theoretical guarantees including generalization bounds, aggregation robustness, and convergence analysis demonstrating that FedPAP optimizes for client-specific performance rather than global consensus. Extensive experiments demonstrate that FedPAP achieves superior performance compared to state-of-the-art methods while reducing communication overhead and achieving 2-4× training speedup, with ablation studies confirming the effectiveness of adaptive pruning and robust aggregation across diverse heterogeneous scenarios.