@Linda108 - I hate to disagree with you but the your "day" begins on the Airbnb site at Check-in time. Offically we rent "nights" so the reservation "day" goes from the Check in time on one day until the Check out time on the next day.
This means if a guest rents for Friday, Jan. 6, they have the right of entry from the posted check in time on Friday, Jan 6 to check out time on Saturday, Jan 7. To me, that means if a guest wants to check on at 2am on Saturday, Jan 7, they must rent from Friday, Jan 6 at check in time.
IF the request is to charge extra for after midnight arrivals, so someone is renting the Friday, Jan 6 night but wants to arrive at 2am on Saturday, you can, by putting it in your House Rules, that there is an extra fee for after-hours check in. You then charge this extra fee to the guest via the Resolution Center.