We don't have synonyms for melkites yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are mellites, melkite and mellite.
(n) :
(since 1724) A member of the Melkite Greek Catholic Church; ellipsis of Catholic Melkite.
(n) :
(since the Great Schism) A member of the Greek Orthodox Patriarchate of Alexandria, the Greek Orthodox Patriarchate of Antioch or the Greek Orthodox Patriarchate of Jerusalem; ellipsis of Orthodox Melkite.
(n) :
(historical) In 5th-century Syria and Egypt, a sobriquet applied to Chalcedonians by their opponents, denoting the Chalcedonians' fidelity to the Byzantine emperor.
(n) :
(since 1724) A member of the Melkite Greek Catholic Church; ellipsis of Catholic Melkite.
(n) :
(since the Great Schism) A member of the Greek Orthodox Patriarchate of Alexandria, the Greek Orthodox Patriarchate of Antioch or the Greek Orthodox Patriarchate of Jerusalem; ellipsis of Orthodox Melkite.
(n) :
(historical) In 5th-century Syria and Egypt, a sobriquet applied to Chalcedonians by their opponents, denoting the Chalcedonians' fidelity to the Byzantine emperor.