Hamilton’s financial system was the first really contentious issue in American politics and would form the direct basis of the First and Second Party systems and dominate politics until the decade before the Civil War. (Related were Hamilton’s fiscal policies, namely, heavy excise taxes and an emphasis on manufactures - both directly opposing Jeffersonian limited government and agrarianism - but these were minor respective to the financial system and mostly undone Jefferson). I am no expert on this topic and most of the below will come from Gordon Woods’s “Empire of Liberty” (esp. Chapter 8) and Ron Chernow’s “Hamilton,” the book on which the musical is based.

Two major elements defined the financial system, both of which Jefferson was unable to dismantle during his presidency. First, key to Hamilton’s strategy of strengthening the federal government over the states was the national debt which would serve 2 purposes: (1) it would allow the Feds to borrow and spend more money on, say, a standing army and expanded bureaucracy, key fixtures in the modern Enlightened European states that Hamilton wanted to replicate in the New World; (2) it would ensure that the government had support from its creditors on who it could rely should the going get tough. The second major plank of Hamilton’s financial system was the Bank of the United States, an institution he similarly envisioned as strengthening the federal government via a vis the states by giving it a primary creditor and as serving an essentially economic function by providing the country with sufficient liquidity via the issuance of paper currency - an essential condition should Hamilton hope to succeed in taking the country in an industrial (read: capital intensive) direction.

Both of these were anathema to the sage of Monticello. Jefferson saw both the bank and the national debt as the epitome of corruption, a state sponsored private corporation (which it was) using the public trust to enrich a small elite sitting on its board and trading in its stock and associated government debt securities at the expense of the little man (an argument that would gain salience as trading in securities quickly caused a financial crisis). It is one of the many ironies of American history that Jefferson, a slaveholding member of the plantation elite, would find himself as the defender of the common man while Hamilton, originally a penniless immigrant, would become the champion of elitism. At its core, Jefferson saw Hamilton’s financial system as a threat to his ideal of agricultural yeomanry and sought to reverse and dismantle it once he ascended to the presidency in 1801. One of Jefferson’s major policies was to stop borrowing (a limitation which he conveniently ignored when pursuing his agenda, such as purchasing Louisiana for $15 million) and quickly pay off the debt. While unsuccessful, he did manage to halve it, taking it from $80 million to $40 million. Jefferson would die before the debt was fully repaid under Andrew Jackson, the only time in American history, a brief situation as the debt was revived under his successor and remains to this day in a form that would make Jefferson want to die again. Less successful was his approach to the Bank - largely due to his own treasury secretary Albert Gallatin favoring the institution - which remained in place until 1811 when its charter expired without renewal. Once again, this situation proved brief and in 1816 the Second Bank of the US was formed after the War of 1812 exposed the weaknesses of the financial system. (Unlike the debt, the reconstituted bank would not prove as resilient, and multiple iterations would come and go before the creation of the Federal Reserve in 1913 which serves similar functions as Hamilton’s brainchild).

For further reading, the bank issue has been so important that more than half the books on antebellum American probably mention it in some form so I would list any more than the two I mentioned above (an inadequate bibliography I know but it is late and the above should be sufficient as an intro).