The Wikipedia page Yellow badge says:
The practice of wearing special markings in order to distinguish Jews and other non-Muslims (Dhimmis) in Muslim-dominated countries seems to have been introduced by Umayyad Caliph Umar II in early 8th century. The practice was reissued and reinforced by Caliph Al-Mutawakkil (847–61), subsequently remaining in force for centuries.[.2]
Source  refers to Jewish Virtual Library:
The introduction of a mark to distinguish persons not belonging to the religious faith of the majority did not originate in Christendom, where it was later radically imposed, but in Islam. It seems that Caliph Omar II (717–20), not Omar I, as is sometimes stated, was the first ruler to order that every non-Muslim, the dhimmī, should wear vestimentary distinctions (called giyār, i.e., distinguishing marks) of a different color for each minority group. The ordinance was unequally observed, but it was reissued and reinforced by Caliph al-Mutawakkil (847–61).
Source [.2] is,
Antisemitism: A Historical Encyclopedia of Prejudice and Persecution, Volume 1 By Richard S. Levy P:779
In the Muslim world, specific markings were used to distinguish and humiliate individuals not belonging to the Islamic faith but dwelling within Muslim-dominated lands. The practice seems to have been introduced by the caliph Omar Il in the early eighth century, although it was unevenly applied throughout the Middle Ages.
Was a practice of making non-Muslims wear special markings introduced by Umar II?