Among the earliest known mermaid myths is that of the Assyrian goddess Atargatis, also called Ataratheh or Derceto. She fell in love with a shepherd, accidentally killed him, and ashamed of what she had done she jumped into a lake. But the water could not conceal her divine beauty, and while she became a fish below the waist she became a woman above it.
She predates the Greek Nereids, Tritons and Sirens, and also Thessalonike, Alexander the Great's sister.
She is said to have originated around 1000 BC, but the earliest representation of her that I have found a reference to is on coinage in Hierapolis in the 4th century BC, and the earliest I have found showing her as part fish and part woman is on a coin from as late as the 1st century BC.