It seems like ちと is more polite since I've seen more people use it. Is it true?
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I disagree that ちと is used more often than ちょっと. Rather than making you sound polite, I think using ちと would just make you sound odd for using such an uncommon word.
ちっと on the other hand is used reasonably often, especially in ちっとも.
If you'd like a more formal version of ちょっと, I think 少し would serve that purpose well in most situations.