Fine-tuning large pre-trained models for downstream tasks has become a fundamental approach in natural language processing. Fully fine-tuning all model parameters is computationally expensive and memory-intensive, especially in resource-constrained environments. Existing parameter-efficient fine-tuning methods reduce the number of trainable parameters but typically overlook the varying sensitivity of different model layers and the importance of training data. In this work, we propose TsqLoRA, a novel method that integrates data-quality-driven selection with sensitivity-aware low-rank adaptation, consisted of two main components: a quality-aware sampling mechanism for selecting the most informative training data, and a dynamic rank allocation module that adjusts the rank of each layer based on its sensitivity to parameter updates. The experimental results demonstrate that TsqLoRA improves fine-tuning efficiency while maintaining or even improving performance on a variety of NLP tasks. Our code will be available at https://github.com/Benjamin-Ricky/TsqLoRA.