About Jason / Jeshua ben Eleazar Maccabeus
He was not the father of Antipas of Idumaea. Sir Anthony Richard Wagner, Pedigree and Progress: Essays in the Genealogical Interpretation of History (1975) lists Antipater I's father as Herodes b c148 BCE.
Jason, "Son of Eleazar; sent by Judas Maccabeus as envoy to Rome (I Macc. viii. 17; Josephus, "Ant." xii. 10, § 6). In the reference to the embassy in II Macc. iv. 11 only Jason's companion, Eupolemus, son of John (or John, son of Eupolemus), is mentioned. G. S. Kr." (JewishEncyclopedia.com, Jason (Jeshua or Jesus))