After you file

I am custodial however we split custody 50/50. Our agreement is one year I claim 2 and he claims one then we will trade off next year. I am just curious if the kids can be on both returns. There is a question on turbo tax that asks if another parent is claiming the child. I said yes but it appears i still got tax credits. When I took his name off my return, that tax credit was no longer available. So is it possible for both to get some credit? They live at our respective homes every other night so it’s 50/50.