This paper focuses on building efficient models for classifying fake news using Large-Language Models (LLMs) based techniques. The approach entails fine-tuning pre-trained LLMs for a low resource language, Tamil. The three models used for the purpose of this study are BERT, RoBERTa and GPT-2 which achieve an accuracy of 0.939, 0.962 and 0.963 respectively. A comprehensive analysis of the fine-tuned models revealed their robustness across different categories of news headlines, including politics, entertainment, and social issues. This robustness implies that even in a variety of scenarios, the models perform well not only in binary classification tasks but also in identifying subtle linguistic clues that differentiate real news from fake. The findings demonstrate how LLM-based methods can significantly increase the quality of Tamil fake news identification, providing insightful information in the field of low-resource language processing and Natural Language Processing (NLP).