In the series, some brotherhoods regularly returned during the games, like the British, the Levantine, or the French brotherhoods. But we never heard of some brotherhoods in countries or eras that were important. These posts will list them.
The East Indies Brotherhood: Locate in South East Asia, this region was a crossroads between many civilizations (Chinese, Japanese, Indian, Javanese) and an economic point of interest for Arab and European merchants. We can imagine that a guild was established in the region since the era of the Hidden Ones.
As Hinduism was the major religion in the area, we can think that the Order of the Ancients was powerful there while they were fading in monotheist Europe and the Middle East. They could support the Majapahit empire, unifying the region under their control. The spreading of Islam between the 12th and the 13th centuries could be the arrival of the Templars. A war between the two Orders could explain the fall of the Majapahit. The treasure fleet of Zheng He could be also a covert operation to recover Pieces of Eden.
In the 16th century, the Portuguese arrived in the region, establishing the Casa da India to regulate the trades in the Portuguese empire. Alfonso de Albuquerque could be a good Templar: viceroy of Portuguese India, he conquered Goa and Malacca. He was also a great navigator, he tried to secure the Indian Ocean for Portugal and established diplomatic relations with Ethiopia, Persia and Thailand.
While the other European countries established trading posts and colonies in South East Asia in the 16th and 17th centuries, surely some European Assassins joined the local Brotherhood making contact with Europe and the Americas as many ships went from South Americas to the Philippines. The organization of the Brotherhood could be similar to the West Indies Assassins with bureaus on the different islands and states and a major headquarters hidden in the jungle. Piracy was also important in the Indian Ocean, so they could be allies of the Assassins.
During the 17th century, the Portuguese's hegemony decreased and the Dutch East India Company became the major power in the area, followed by the British East India Company during the 18th-19th century. As the European states took direct control of the region in the 19th century, independence movements increased in South East Asia to fight colonization. The Assassins could be there.
During WW2, the Japanese Empire invaded the region defeating the Allies' forces. The Assassins could help the resistants and later promote the independence of the countries during the Cold War.