Napoleon clearly won the election, and should be the next president. Tweed's challenge utterly lacks legitimacy and is tantamount to a coup.
Tantamount to? According to Edward Luttwak, "[a] coup consists of the infiltration of a small, but critical, segment of the state apparatus, which is then used to displace the government from its control of the remainder." The military/paramilitary is not necessary to a coup. Since the Supreme Court (a small, but critical, segment of the state apparatus) is controlled by Tweed voters, they can use that to displace the government (the rest of the government, including Napoleon) from control of the rest of it (such as the Presidency). It
is a coup.