If I have custody of children whose father I never married, can I claim them as qualifying children?a

My ex-fiance and I have 50/50 custody of our three children. The oldest two are not biologically mine, and as their father and I never married, I’m not sure what the legal term for the IRS would be. Our custody papers state that in odd-numbered tax years, I get to claim one of my non-biological children, but can I claim him as a qualifying child? I don’t know if he’s technically my “stepchild”, but I was granted custodial rights by the court.