It is certain that Jesus, a Jew residing in the land of Israel in the first century, did not wear a kippah (skullcap).
The custom of wearing a kippah 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 מִגְבַּעַת (migba’at, a turban-like headdress; see Exod. 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 bareheaded. 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.