Joe Biden may have an ancestral connect with Christopher Biden who was a captain in the East India Company but there is no evidence to ascertain it.
As per Tim Willasey-Wilsey, a visiting professor at the Department of War Studies, King’s College, London there are no records of a George Biden in India but there were two Bidens who were brothers who became Captains of East India Company armed merchant ships. William Henry Biden started out in the Midas (414 tons) and went on to command the ships Anna Robertson, Ganges, and Thalia (570 tons) before he died of a stroke at Rangoon on 25th March 1843 aged 51.
Christopher Biden had a more illustrious career and was well-known in Chennai. By 1807 he was sailing in the 1333 ton Royal George which made seven return voyages to India before 1818. By 1815 he had become its Chief Mate. In 1821 he became Captain of the Princess Charlotte of Wales and made four return journeys between England and Calcutta. He also captained the new Royal George (1426 tons) on one voyage. Each return journey lasted a year. In 1830 he retired from the Princess Charlotte and settled down in Blackheath, near London. He moved back to India in 1839 and worked as a Master Attendant and Marine Storekeeper at Madras; in charge of shipping and spent 19 years there. He died in Madras in 1858. According to Wilsey, Christopher Biden is the most likely candidate if Joe Biden indeed had an ancestor in India but due to the lack of concrete evidence, we have marked this claim unverifiable.