Fine-tuning large language models is essential for task-specific adaptation, yet it remains computationally prohibitive. Parameter-Efficient Fine-Tuning (PEFT) methods have emerged as a solution, but current approaches typically ignore the distinct roles of model components and the heterogeneous importance across layers, thereby limiting adaptation efficiency. Motivated by the observation that Rotary Position Embeddings (RoPE) induce critical activations in the low-frequency dimensions of attention states, we propose RoPE-aware Selective Adaptation (RoSA), a novel PEFT framework that allocates trainable parameters in a more targeted and effective manner. RoSA comprises a RoPE-aware Attention Enhancement (RoAE) module, which selectively enhances the low-frequency components of RoPE-influenced attention states, and a Dynamic Layer Selection (DLS) strategy that adaptively identifies and updates the most critical layers based on LayerNorm gradient norms. By combining dimension-wise enhancement with layer-wise adaptation, RoSA achieves more targeted and efficient fine-tuning. Extensive experiments on fifteen commonsense and arithmetic benchmarks demonstrate that RoSA outperforms existing mainstream PEFT methods under comparable trainable parameters. The code is available to ease reproducibility at https://github.com/Applied-Machine-Learning-Lab/RoSA.