It sounds like you are in a position that actually should be getting overtime pay, but your supervisor is wanting to treat it as comp time instead (which is what some positions do, but if that was the case he would have you enter the time accurately and correctly).

Based on this, I am assume for you are working for a university and the PI doesn’t have the right type of funds to pay overtime. I have seen PIs try to do this, and it is a huge issue for HR because it is illegal. I would talk to HR about it - either they will find the money to pay you overtime or you won’t be required to work overtime any more. Either way, I think it’s a win for you and and you’ll get to know you are doing things the right way.