Large language models (LLMs) have made exciting achievements across various domains, yet their deployment on resource-constrained personal devices remains hindered by the prohibitive computational and memory demands of task-specific fine-tuning. While quantization offers a pathway to efficiency, existing methods struggle to balance performance and overhead, either incurring high computational/memory costs or failing to address activation outliers—a critical bottleneck in quantized fine-tuning. To address these challenges, we propose the Outlier Spatial Stability Hypothesis (__OSSH__): _During fine-tuning, certain activation outlier channels retain stable spatial positions across training iterations._ Building on OSSH, we propose __Quaff__, a Quantized parameter-efficient fine-tuning framework for LLMs, optimizing low-precision activation representations through targeted momentum scaling. Quaff dynamically suppresses outliers exclusively in invariant channels using lightweight operations, eliminating full-precision weight storage and global rescaling while reducing quantization errors. Extensive experiments across ten benchmarks validate OSSH and demonstrate Quaff’s efficacy. Specifically, on the GPQA reasoning benchmark, Quaff achieves a 1.73× latency reduction and 30% memory savings over full-precision fine-tuning while improving accuracy by 0.6% on the Phi-3 model, reconciling the triple trade-off between efficiency, performance, and deployability. By enabling consumer-grade GPU fine-tuning (e.g., RTX 2080 Super) without sacrificing model utility, Quaff democratizes personalized LLM deployment. The code is available at https://anonymous.4open.science/r/Quaff-B322/.