There are no tax credits for having a child dependent unless you have actual physical custody more than half the nights of the year, or you have a signed waiver from the parent who does have actual physical custody more than half the nights of the year. (No matter what your state court order says, the IRS follows this rule from federal law.)
If you are the non-custodial parent and you do have a signed waiver, you can claim the child tax credit (up to $2000). But the ability to claim earned income credit and use head of household status always stays with the custodial parent and can't be waived or transferred.
If you were eligible to claim your child as a dependent in the past (because of a waiver), but you did not, you could file an amended return for 2021, 2022 or 2023. Older years are too old to amend. As far as future years is concerned, each tax return is based on the facts of that particular year, and what you claimed or did not claim in the past, has no effect on what you are eligible to claim this year based on this year's facts.
