Can I claim my noncustodial parent's unearned income tax credit if I haven't claimed it in a few years?

[xmasbaby0]

There is no such thing as "unearned tax credit."   Do you mean the earned income credit----the credit you get if you are the custodial parent and have income from working?   The only way to get a credit from a past year is to amend your tax return for the past year--or for each of the past years if you were eligible for it.   If you were the NON-custodial parent, you were not eligible to get the earned income credit.  That credit goes to the parent with whom the child spent the most number of nights---at least 183 nights in the tax year.   The NON-custodial parent might be able to get the child tax credit but only if there was a signed form 8332 allowing the child tax credit for the non-custodial parent.

Please explain your circumstances so we understand, and then we can provide more clarity.

[Opus 17]

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. 

[Opus 17]

Are you saying that your parent may have been eligible for something, and you are asking if you can claim it instead?  No.  Whatever you can claim on your tax return is based on your personal facts--income, deductions, credits, etc.  You can't claim a credit that would have gone to someone else, even if they didn't claim it.