There is no mention of this in the relevant scriptures.
The Book of Esther does not mention any children of Esther.
Historically, King Xerxes I had several children by various wives, but does not seem to have ever been married to either Vashti or Esther.
After Esther broke her secret, thar she was a Jewess (female Jew), King Ahasuerus probably did not have more than one Hebrew Prince and one Hebrew Princess.