1. Jyotirindra Basu
Known as Jyoti Basu was an Indian politician belonging to the Communist Party of India (Marxist) from West Bengal, India. He served as the Chief Minister of West Bengal state from 21 June 1977 to 8 Nov 2000, making him the longest-serving Chief Minister in the country's history. ( According to Quora user Aminul Aslam )
2. Pawan Kumar Chamling
He is the fifth and incumbent Indian chief minister of Sikkim. Chamling is the founder president of the Sikkim Democratic Front, which has governed the state for five successive terms since 1994. On 28 April 2018 he is set to be India's longest serving Chief Minister ever.