If I claim my daughter this year would I get the child tax credit when I did not receive it for her this year her father who claimed her last year did?

If you claim your daughter this year, you will get the Child Tax Credit.  You will want to say you did NOT get the advanced payments because the father received them.  When he files his tax return and does not claim her, he may have to pay back the advancements he received.   

 

From the IRS: 

If you qualify for repayment protection, the amount of your tax liability from excess advance Child Tax Credit payments is reduced by up to the full repayment protection amount. The full repayment protection amount equals $2,000, multiplied by the following:

• The number of qualifying children that the IRS took into account in determining the IRS’s initial estimate of your advance Child Tax Credit payments, minus
• The number of qualifying children properly taken into account in determining the allowed Child Tax Credit amount on your 2021 tax return.

Example: You properly claimed three qualifying children on your 2020 tax return, but claim only one qualifying child on your 2021 tax return. You can receive up to $4,000 in repayment protection (that is, $2,000 for each excess qualifying child) if you qualify.

You will be able to apply the full repayment protection amount of $2,000 for each excess qualifying child if your modified adjusted gross income (AGI) is at or below the following amounts based on the filing status on your 2021 tax return:

• $60,000 if you are married and filing a joint return or if filing as a qualifying widow or widower;
• $50,000 if you are filing as head of household; and
• $40,000 if you are a single filer or you are married and filing a separate return.

Since you didn’t received the advanced child tax credit (I assume that is what you are referring to) answer “no”. When he files he would answer “yes” and report the amount he received. Depending on his income he might have to pay all or some of that credit back. 

Answer the interview questions carefully and accurately. It's quite possible you can Both get the credit. Reason: Advance payments were based on Projected dependent claims. Actual entitlements will b allocated based on your 2021 returns.