A mermaid was a being that was half-humanoid, half-fish who lived under the sea, depicted in Hans Christian Andersen's The Little Mermaid.
In 2370, Melora Pazlar was unfamiliar with the term when Jadzia Dax compared the main character of The Little Mermaid's dilemma with hers. (DS9: "Melora")
Mermaids lived on the planet Golos Prime in the Clevari system. Q, Junior suggested taking a dip with these mermaids, during a brief visit to their system in 2377. (VOY: "Q2")