You don't mention the child that your BF claimed to get the AdvCTC. If he is your dependent for 2021, he will not be able to claim his child on his tax return. A dependent can not have a dependent.
The CTC for the child is much bigger than the "other dependent credit" ($500 max) that you get for your BF being your dependent.
You can not claim an unrelated person as a dependent, unless he lived with you all year.
