Either is acceptable.

Jeez(e). It is a corruption of Jesus, one of many. Gee, gee whiz(z)...geewhillikins is a fanciful substitute for Jerusalem. Most of these date back to the late 19th century. Jeez(e), which is American slang for gee, dates back to 1923. The reason geez is incorrect, is that, well for starters, it's another word. Geez, is the ancient language of Ethiopia, and is still used as a liturgical language today. While "geez" and "geeze" are in the urban dictionary as alternate spellings for jeez, they haven't come into popular usage enough to be introduced to dictionaries and the English language beyond street and online slang. Maybe at some point these spellings will be accepted as alternate spellings for jeez(e), but until they are they're incorrect. Remember, you're now talking about the misspelling of a word that is already slang based on a word that's a shortening of an exclamation. And that spelling already belongs to a word and it's pronounced differently. Why make life more complicated than it already is? Just spell it jeez or jeeze and leave it there. And an additional note, while both jeez and jeeze are correct spellings, jeez is the more commonly used one and the more commonly known one so I'd go with that.