The dependent interview is tricky, particularly in divorce situations. You must follow the interview carefully.
Mostly, you must give up the notion that you "share 50/50". In particular, do not select that the child lived with you 6 months. TurboTax (TT) will give you a warning that it will treat 6 months as LESS than half the year, thereby treating you as the non-custodial parent. Pick 5 or 7 months.
For tax purposes, there is no such thing as joint custody, regardless of what your legal agreement says. The requirement, to be custodial parent, is that the child live with you MORE than 50% of the time. One of you has to be the custodial parent and the other the non-custodial parent. The IRS goes by physical custody, not legal custody.
In the rare case (could probably only happen in a leap year like 2024), where the time that each parent has the child is exactly equal, then the parent with the higher income (AGI) is the custodial parent, for the purpose of determining who has first priority on claiming the child as a dependent. But then neither parent can claim a Qualifying Child dependent, for some tax benefits because neither parent had the child the required MORE than half the year. (no earned income credit, based on that child, and the child would not qualify the parent for Head of Household filing status).
There's another thing to understand in your situation.
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/exemption/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.
So, it's good idea to let the other parent know that you will be claiming those items, as she may think she is entitled to them (and may well be entitled to them).
Ref: https://www.irs.gov/publications/p17#en_US_2017_publink1000170897
Scroll down to "Children of divorced or separated parents (or parents who live apart)"
Yes, the IRS expects you to count the numbers of nights the child sleeps at each parent's home.
It is allowed for you to arrange the child's schedule so that the child spends more than half the year with the father one year and more than half with the mother the next year so that you are each the custodial parent in the year you claim the child, so that you can claim full benefits.
