No, Aaron Burr was the "running mate" of Thomas Jefferson in the presidential elections of 1796 and 1800 (the election process did not actually support the concept of the vice presidential running mate until the 1804 ratification of the 12th Amendment to the U.S. Constitution).
John Adams was the only Federalist U.S. President. Aaron Burr was the second Democratic-Republican U.S. Vice President.
John Adams belonged to the Federalist party, which was in existence from the 1790s to about 1816.
democratic republican party
Federalist
He switched to Democratic- Republican. He first belonged to the Federalist Party.
John Adams
He was Federalist.
There were no political parties in 1789.
Federalist
Federalist
John Quincy Adams supported his father and the Federalists when he was young.
whig
Federalist