To follow-up on the comments from @xmasbaby0, if the child lived with you for the longer part of the year compared to the mother, under IRS rules, you would be deemed to be the custodial parent regardless of whatever agreement you had with the mother regarding your child. If the mother (assuming the mother is the non-custodial parent) wants to claim an exemption for the child, and claim the child tax credit, and the additional child tax credit, you will need to release your claim to those credits by completing Form 8332. After completing Form 8332, you will need to give it to the mother because the mother must include it with their return each year the exemption is claimed.
Even if you complete Form 8332, and give it to the mother, the mother will not be able claim head-of-household filing status, the credit for child and dependent care expenses, the exclusion for dependent care benefits, the earned income tax credit, or the health coverage tax credit, as those credits, if applicable, remain with the custodial parent.
@bayerngrl1
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