The past tense of ‘babysit’ is ‘babysat’.
‘Babysit’ is a regular verb, which means it changes to ‘babysat’ when referring to an action that has already taken place. For example, if you took care of a child yesterday, you would say, ‘I babysat for my neighbor last night.’ This is a typical example of vowel change in the past tense formation, which is common in English.