incorrectly has 3 distinct synonyms spread across 2 of its 2 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is correctly.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
in an incorrect manner
“to credit Lister with the first formulation of the basic principle of stratigraphy would be to bestow credit falsely”
Synonyms, antonyms and the broader and narrower relations for incorrectly come from Princeton University’s WordNet. Full sources and licences.