Hmmmm.
Heritage of COH IV Iudaeorum Equitata
By way of an idea: During the Alexandrine War, Julius Caesar depended on auxiliaries from the Eastern client states to bail him out of a tight spot his support for Cleopatra landed him in. Among them were forces from Jusaea who distinguished themselves by bravery and reliability. Caesar, whoi had considerable respect for them, took a cohort of them into his service and maintained them alongside hios Germanic horse guards.
Augustus, having inherited Ceasar's retinue, decided to keep them in his service. He cultivates good relations with the Jews of Italy and the Hasmonaean family and can rely on their support in the taking of Alexandria. As a result - big POD - he exempts the Jews from the dilectus, but allows the to form auxiliary military units that accommodate their usages. They serve in and around Judaea and Syria along the Euphrates and desert frotnier
In the course of the Claudian reform, the Roman army regularises COH IV Iudaeorum Equitata (the original Caesarean unit), I, II and III Iudaica Sagittariorum, V-VI Iudeaorum, I-III Samaritorum and Ala I Iudaeorum.
During the revolt, II Iudaica Sagittariorum and VI Iudaeorum join the rebels. The remaining Jewish units remain loyal, but are distributed across other provinces, mainly the west. Their recruitment continues to be primarily (not exclusively) from among Jewish communities, and Jewish veterans settle around their bases.
By the third-century crisis, it is taken for granted that the Jews are a martial race. Units of Jews are raised and integrated into the Diocletianic army, old ones retained, and non-Jewish units make efforts to accommodate Jewish recruits. Their status remains unaffected iunder the Christian emperors and both in the East Roman Empirew and the Western successor states it is assumed that the Jews are allowed to retain their faith and practises in return for their traditional military service. Jewish quarters in cities raise militias for their kings and both the Frankish and Visigothic kings maintain Jewish bodyguards.
By the Middle Ages, Jewish communities are obligated to render military service to secular lords. Especially the Holy Roman Emperors are able to raise fearsome armies of 'Kaiserjuden'. They can not own land or hold civil office, and participation in craft guilds and the professions is increasingly limited by law. The only option for a young Jew to rise in the world (other than the rabbinate) is the military. Many Jewish war leaders combine literary education and administrative skill with terrifying bravery and legendary aggressiveness. Among the most famous are Isaac of Braunschweig, commander of Henry the Lion's Jewish archers, Salomon Apulus, Frederick II's legendarily skilful and inventive siege engineer, Josue ben Benjamin, admiral of House Berenguer and conqueror of the Balearics, Jonathan Bellister, Edward III's captain of artillery, and 'Metzen-Hansel' Bacharach, captain of Charles IV's life guards.
Not many European nations follow the exhortations of the Vatican to deny the Jews trust and rank, and only the most extreme cases of piety in rulers ever lead even to temporary bans on their employment. By the 18th century, many Jewish families have generation-long traditions of military service and most armies either allow them to serve like Christian soldiers (both Austrian Marschall Bendavid Graf von Theilenhofen and Prussian artillery general von Levin were prominent Jews), or grant them separate career opportunities (Maitre d'Escadre Jean-David Lemuel was commander of the Brest squadron without ever receiving a commission).