Complex sentence: Burr certainly knew of Hamilton's opposing his ascension to the U.S. Presidency in 1800, and may have suspected, in substance, Hamilton's confidential statements against him, such as those enumerated in Hamilton's private letter to Supreme Court Justice Rutledge.
Split into simpler sentences: Burr certainly knew of Hamilton's publicly opposing his ascension to the U.S. Presidency in 1800. Hamilton made confidential statements against him, such as those enumerated in Hamilton's private letter to Supreme Court Justice Rutledge.