If a registered domestic partner is the stepparent of his or her partner’s child under state law, the registered domestic partner is the stepparent of the child for federal income tax purposes.
IRS website Q8 - https://www.irs.gov/newsroom/answers-to-frequently-asked-questions-for-registered-domestic-partners-...
If this is the case for your situation then you are eligible for the Child Tax Credit if the child is under the age of 17 in 2022.
Any child care expenses for the child can be entered on your tax return for the expenses you paid for the childcare so that you can work, if the child is under the age of 13.
If both of you and your partner lived in the same home and the child lived in the same home for over one-half of the year then you would select the child lived with both parents.
If you are not the custodial parent of your own child, meaning the child did not live with you for over one-half the year, then you need to have a Form 8332 signed by the custodial parent relinquishing their claim to the exemption to the child so that you can claim the child as your dependent.
