did [Yahushua] wear a kippah?
by Shmuel Safrai - Jerusalem Perspective. Professor of Jewish History at the Hebrew University
It is certain that [Yahushua], a Jew residing in the land of Israel in the first century, did not wear a kippah or skullcap. This custom arose in Babylonia between the third and fifth centuries C.E. among the non-Jewish residents - Jewish residents of Babylonia had not yet adopted this custom, as the Dura-Europos frescoes show - and passed from there to the Jewish community of Europe.
Although priests wore a tibgm (mig BA 'at, a turban-like headdress (Ex 28:4, 40; Lev 8:13), other Jews of the Second Temple period did not wear a headcovering. This is confirmed both by the literature and archaeological remains of the period. For instance, the reliefs on the Arch of Titus in Rome, which depict the victory procession in Rome following the conquest of Jerusalem in 70 C.E., show the Jewish captives bare headed. Likewise, the frescoes of the mid-third century C.E. synagogue excavated at Dura-Europos represent all the Jewish men as bareheaded except for Aaron the priest.
Contemporary Jewish sources verify the picture presented in the New Testament: "Every man who prays or prophesies with his head covered dishonours his head. And every woman who prays or prophesies with her head uncovered dishonours her head - it is just as though her head were shaved . . . A man ought not to cover his head, since he is the image and glory of [Elohim]; but the woman is the glory of man" (I Cor 11:4-7).
According to the Babylonian Talmud, Nedarim 30b, Jewish children were always bareheaded, men sometimes covered their heads and sometimes did not, while women covered their heads at all times. But it must be remembered that this is a late source (end of fifth century C.E.) and reflects Jewish practice in Babylonia.
According to the Shulhan Arukh, the sixteenth-century code of Jewish law compiled by Rabbi Joseph Karo, one should not walk bareheaded even four cubits (two metres) (Orah Hayyim 2:6). This ruling is derived from the Babylonian Talmud, Kiddushin 31a, where it is stated that Rav Huna (fourth century C.E.), the son of Rav Yehoshua, would not walk bareheaded four cubits (cf. Babylonian Talmud, Shabbat 118b). However, this is noted as the exceptional practice of a particular sage, not as a practice observed by all males. The practice of covering one's head in public apparently was not yet wide-spread in Babylonia in the fourth century C.E.