Large Language Models (LLMs) have shown promising capabilities in handling clinical text summarization tasks. In this study, we demonstrate that a small open-source LLM can be effectively trained to generate high-quality clinical notes from outpatient patient-doctor dialogues. We achieve this through a comprehensive domain- and task-specific adaptation process for the LLaMA-2 13 billion parameter model. This process incorporates continued pre-training, supervised fine-tuning, and reinforcement learning from both AI and human feedback. We introduced an enhanced approach, termed DistillDirect, for performing on-policy reinforcement learning with Gemini Pro serving as the teacher model. Our resulting model, LLaMA-Clinic, is capable of generating clinical notes that are comparable in quality to those authored by physicians. In a blinded physician reader study, the majority (90.4%) of individual evaluations rated the notes generated by LLaMA-Clinic as "acceptable" or higher across all three criteria: real-world readiness, completeness, and accuracy. Notably, in the more challenging "Assessment and Plan" section, LLaMA-Clinic scored higher (4.2/5) in real-world readiness compared to physician-authored notes (4.1/5). Additionally, we identified caveats in public clinical note datasets, such as ACI-BENCH. We highlight key considerations for future clinical note-generation tasks, emphasizing the importance of pre-defining a best-practice note format. Overall, our research demonstrates the potential and feasibility of training smaller, open-source LLMs to assist with clinical documentation, capitalizing on healthcare institutions' access to patient records and domain expertise. We have made our newly created synthetic clinic dialogue-note dataset and the physician feedback dataset publicly available to foster future research in this field.