Please explain more. Are you and the other parent married and are you filing separate tax returns? Or are you divorced or never married/ unmarried? Who claimed the child on their 2021 tax return? Who did the child live with the most in 2021? We do not know enough to say whether you should claim the child and the child tax credit for 2021.
There is a way to split the tax benefits. For future negotiations with the other parent (and maybe even for this year) the following info may be of use:
There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.
Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the dependency to him.
Note that the special rules mentioned above only apply if you live apart from the other parent – separated, divorced, or never married.
If you live together unmarried with the other parent of your child, you can’t split the tax benefits and only one parent may claim the child on their tax return. That parent claims everything, and the other parent must leave the child off their return completely.