There was no modern banks in Colonial America era. The Colonial Americans used banks in England and gave credit to each other without banks. Until 1781, Alexander Hamilton wrote to Robert Morris, who is the Finance Superintendent in the congress, to recommend a central bank to be founded. The unusual US banking system in the 1800s was a result of the political instability and the different political interests within the US, as well as that the banks in New York held too much power and became too vulnerable when the crisis came. Most banks back before 1781 were businesses chartered by state legislature. So they were highly influenced by the state governments. The emergence of the Bank of the United States, founded by Hamilton, was controversial
