An archaism is an adoption or imitation of archaic words or style.

the use of older or obsolute form

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Walter Eugene Foster has written:

'Studies in archaism in Aulus Gellius' -- subject(s): Latin language, Archaisms, Language

I would write "Jesus's." Some prefer "Jesus'."

"Jesus's" is always acceptable. Some authorities permit "Jesus' " as an accepted archaism. ("Jesus' " could also refer to something belonging to a family named Jesu, as in, "the Jesus' house, where George Jesu and his parents live.")

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