To claim the child as a dependent, you and the child must live in the same home for more than half the number of days it is alive in 2020. If you and the mother both qualify under this rule, only one of you can claim the child. The other parent should leave the child completely off their tax return. It doesn't matter what the address on your tax return is -- that's only for where you want the IRS to send any checks or letters.
In Turbotax, select that the child lived with you "all year" -- that is the correct answer for a child born during the year. Do not answer "yes" that you have a custody agreement, that only applies to a court order between parents who are divorced or separated.
