Background: Clinical documentation represents a significant burden for healthcare providers, with physicians spending up to 2 hours daily on administrative tasks. Recent advances in large language models (LLMs) offer promising solutions, but privacy concerns and computational requirements limit their adoption in healthcare settings. Objective: To develop and evaluate a privacy-preserving, on-device medical transcription system using a fine-tuned Llama 3.2 1B model capable of generating structured medical notes from medical transcriptions while maintaining complete data sovereignty entirely in the browser. Methods: We fine-tuned a Llama 3.2 1B model using Parameter-Efficient Fine-Tuning (PEFT) with LoRA on 1,500 synthetic medical transcription-to-structured note pairs. The model was evaluated against the base Llama 3.2 1B on two datasets: 100 endocrinology transcripts and 140 modified ACI benchmark cases. Evaluation employed both statistical metrics (ROUGE, BERTScore, BLEURT) and LLM-as-judge assessments across multiple clinical quality dimensions. Results: The fine-tuned OnDevice model demonstrated substantial improvements over the base model. On the ACI benchmark, ROUGE-1 scores increased from 0.346 to 0.496, while BERTScore F1 improved from 0.832 to 0.866. Clinical quality assessments showed marked reduction in major hallucinations (from 85 to 35 cases) and enhanced factual correctness (2.81 to 3.54 on 5-point scale). Similar improvements were observed on the internal evaluation dataset, with composite scores increasing from 3.13 to 4.43 (+41.5%). Conclusions: Fine-tuning compact LLMs for medical transcription yields clinically meaningful improvements while enabling complete on-device browser deployment. This approach addresses key barriers to AI adoption in healthcare: privacy preservation, cost reduction, and accessibility for resource-constrained environments.