BACKGROUND: Medical large language models (LLMs) have demonstrated remarkable performance in answering medical examinations. However, the extent to which this high performance is transferable to medical questions in Spanish and from a Latin American country remains unexplored. This knowledge is crucial as LLM-based medical applications gain traction in Latin America. AIMS: To build a dataset of questions medical examinations taken by Peruvian physicians pursuing specialty training; to fine-tune a LLM on this dataset; to evaluate and compare the performance in terms of accuracy between vanilla LLMs and the fine-tuned LLM. METHODS: We curated PeruMedQA, a multiple-choice question-answering (MCQA) dataset containing 8,380 questions spanning 12 specialties (2018-2025). We selected ten medical LLMs, including medgemma-4b-it and medgemma-27b-text-it, and developed zero-shot task specific prompts to answer the questions. We employed parameter-efficient fine tuning (PEFT) and low-rand adaptation (LoRA) to fine-tune medgemma-4b-it utilizing all questions except those from 2025 (test set). RESULTS: Medgemma-27b showed the highest accuracy across all specialities, achieving the highest score of 89.29% in Psychiatry; yet, in two specialties, OctoMed-7B exhibited slight superiority: Neurosurgery with 77.27% and 77.38, respectively; and Radiology with 76.13% and 77.39%, respectively. Across specialties, most LLMs with <10 billion parameters exhibited <50% of correct answers. The fine-tuned version of medgemma-4b-it emerged victorious against all LLMs with <10 billion parameters and rivaled a LLM with 70 billion parameters across various examinations. CONCLUSIONS: For medical AI applications and research that require knowledge bases from Spanish-speaking countries and those exhibiting similar epidemiological profile to Peru's, interested parties should utilize medgemma-27b-text-it.