King Nebuchadnezzar, the head of Babylon, was the son of King Solomon and Queen Sheba. This is recorded by the Jews and there is no reason to disbelieve it. Apparently this information is also supposed to be in the book, Legends of the Jews.
From the Jewish Encyclopedia,
Nebuchadnezzar, the "wicked one" ("ha-rasha'"; Meg. 11a; Ḥag. 13b; Pes. 118a), was a son—or descendant?—of the Queen of Sheba by her marriage with Solomon ("Alphabet Ben Sira," ed. Venice, 21b; comp. Brüll's "Jahrb." ix. 9), and a son-in-law of Sennacherib (Targ. to Isa. x. 32; Lam. R., Introduction, 23, says "a grandson"),
King Solomon must have married Queen Sheba, whom the Quran describes as a "practicing witch". She came to King Solomon to learn about his wisdom ending up as one of his wives.
They had a son that would produce the nation or kingdom called BABYLON.