The practice of fasting on the 13th of Adar originated in geonic Babylonia. The responsum of R. Natronai is the earliest Babylonian geonic source that refers to the fast by a name, calling it Ta‘anit Purim. Of the four sources in the geonic period from Babylonia and its environs that refer to the fast by a name, most likely none of them calls it Ta‘anit Esther.
When the geonic sources express or imply something about the origin of the fast, they consistently state or imply that the fast is a rabbinic obligation dating from the biblical period. The approach most consistent with the geonic sources is that the fast arose as a consequence of an interpretation of M. Megillah 1:1–2 (“second approach”). It has been suggested that the authors of the interpretation were responding to and opposing widespread practices of fasting on Shabbat and Erev Shabbat. This led them to interpret M. Megillah 1:1–2 to imply a prohibition of fasting on Shabbat and Erev Shabbat. The result was a new “tradition” about an ancient fast on the 13th of Adar. There had not been a practice of fasting on the 13th at the time the geonic interpretation of M. Megillah 1:1–2 originated.
Mitchell Furst, “The Origin of Ta’anit Esther”, AJS Review 34, No. 2 (November 2010), 344-345.