It is very uncommon to use this term in identifying the RELIGION of the Jewish people.
Historically, the Title JEW applied specifically to all those who were born in the Kingdom of Judea from c. 949 BCE to 135 CE.
Contrary to all other spurious explanations, this was and is exactly what their religion is:
the followers of the faith and laws as handed down to Moses in the Torah
(the Five Books of Moses/ Pentatuch).
Those who follow Buddha are called Buddhists.
Those who follow Zoroaster are called Zoroasterians.
Those who follow Jesus are called Christians or Jesuits, etc.
Those who follow Muhammad are called Muhammadans.
Any person who professes and or follows the Law of Moses is called in Arabic, Mousawi.
Every Mousawi/Jew is a Muslim, since they fervently and unwaveringly believe in the One and Only God.
The Israelites - and their descendants, the Jews - are the true and original Muslims since they were the ones chosen by God to believe in Him twenty one centuries before Muhammad and his new cultic belief syatem appeared on the scene.
It is very illuminating to bring to the attention of the reader the following fact:
The Jews in the Arab countries such as Iraq & Syria are identified as al Ta'ifa al Moussawyia meaning the Sect of Moses.
Accordingly, in English, the religion of the Jew would be called Mosaic.