Modern Jews are not the descendents of Judah of the Bible.
Their story begins with Esau, the twin brother of Jacob, the father of the 12 tribes of Israel. He had a quarrel with Jacob, Jacob fled and in the meantime Esau took canaanites as wifes
>1This is the account of Esau (that is, Edom). 2Esau took his wives from the daughters of Canaan: Adah daughter of Elon the Hittite, Oholibamah daughter of Anah and granddaughter of Zibeon the Hivite, 3and Basemath daughter of Ishmael and sister of NebaiothThese and their descendents are the known as the Edomites. Among the Edomites there are the Amelek
>12Additionally, Timna, a concubine of Esau’s son Eliphaz, gave birth to Amalek. These are the grandsons of Esau’s wife Adah.which later became the enemy of Israel and are seen as their eternal nemesis.
This is who they are, but how did they become known as the Jews, the descendents of Judah and Israel?
https://en.wikipedia.org/wiki/Edom>The Edomites first established a kingdom ("Edom") in the southern area of modern-day Jordan and later migrated into the southern parts of the Kingdom of Judah ("Idumea", or modern-day southern Israel/Negev) when Judah was first weakened and then destroyed by the Babylonians, in the 6th century BC.The original ones were conquered by Babylon and carried away. The Edomites settled there and took things over, and after the original Judahites returned they fought and eventually
>They were again subdued by John Hyrcanus (c. 125 BC), who forcibly converted them, among others, to JudaismNotethat "Judaism" isnt here the modern Judaism.
Somewhere in the meantime the Pharisee were founded whichs tradition is based on the oral law which became the talmud and very likely was influenced by babylonian teachings the Judahites brought back and is the foundation of modern Judaism
https://en.wikipedia.org/wiki/Pharisees>The Pharisees preserved the Pharisaical oral law in the form of the Talmud 
