Deductions & credits

The rules are in publication 501.

https://www.irs.gov/pub/irs-pdf/p501.pdf

An important concept is that the IRS follows federal law, which is summarized in the publication.  The IRS, for the most part, doesn't care about state custody orders or state courts since federal law overrides state law.

For a biological parent, the key fact is where did the child spend more than half the nights of the year?  If the child spent more than half the nights of the year in your home (or half the days if you work nights) then you are the only person with the automatic right to claim the child as a dependent.  You don't have to prove how much support you provided, and you don't have to worry about custody orders or other people who have or had parental rights.  (For temporary absences like summer camp or trip to grandma's house, the child is credited with living with you if they would have been living with you except for the temporary absence.)

However, a foster parent (as long as the child was placed by the court or other state-approved process) has the same rights as a biological parent.  If your child was in foster home, then both parents need to count the number of nights where the child physically lived -- whoever has more than half the nights (183 or more) claims the child.  End of debate.

Other individuals who might have custody (other family members, for example) may or may not have the same rights as a biological parent depending on how closely related they are.   You would have to provide more information or read publication 501.  

But in short, if you are asking about the upcoming 2025 tax return, the key question is whether or not your child lived under the same roof as you for 183 or more nights in 2025.