If I'm going into the campsite during the days of my reservation, is there an entry fee each time I leave and come back?

The state parks in New York are once a day fees no matter how many parks you visit for the day just keep your receipt!

Nope, they give you a tag for your car when you check into your camping reservation, you show that every time you re-enter instead of paying an entry fee every time. The tag covers all the days from the start to the end of your reservation.