vice president: Thomas Jefferson
Clarification:
The US official appointment of 1796 was the primary question and the main one where the president and vice president were chosen from various gatherings.
John Adams ran for president through the Federalist Party (or Government Party) alongside Thomas Pinckney. Even though Adams was the person who won, Thomas Jefferson, of the Majority rule Conservative Alliance of the US, got a larger number of votes than Pinckney, so he was chosen vice president.
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