His education was paid for by a stipend donated by the St. Croix business community. They had hopes he might become a doctor and return to the island to set up practice. Must be thinking about Hugh Knox, a Presbyterian minister, a graduate of the College of New Jersey, who some think was responsible for motivating the St. Croix business people to set up Hamilton's stipend.
His earlier education was done privately by a local Jewess. His family history probably kept him out of the local religious school.
A letter written to Edward Stevens from the West Indies during Hamilton's early employment at the counting
house.http://www.law.umkc.edu/faculty/projects/ftrials/burr/HamLettertoFriend.htm