Not, if you act now.  In order to get the child Recovery Rebate Credit the child must qualify for the Child Tax Credit.  Since the children are not related to you they would not qualify.  However, they would qualify as his dependents (see criteria below).

If you have already filed, you have a unique one-time opportunity to make a correction to your 2020 return without amending.  Use this link to have your tax return sent back to you before 6 February.  Make the corrections and resubmit.

 The child qualifies you for the CTC if the child meets all of the following conditions.

1. The child is your son, daughter, stepchild, eligible foster child, brother, sister, stepbrother, stepsister, half brother, half sister, or a descendant of any of them (for example, your grandchild, niece, or nephew).

2. The child was under age 17 at the end of 2020.

3. The child did not provide over half of his or her own support for 2020.

4. The child lived with you for more than half of 2020 (see Exceptions to time lived with you , later).

5. The child is claimed as a dependent on your return. See Pub. 501 for more information about claiming someone as a dependent.

6. The child does not file a joint return for the year (or files it only to claim a refund of withheld income tax or estimated tax paid).

7. The child was a U.S. citizen, U.S. national, or U.S. resident alien. For more information, see Pub. 519, U.S. Tax Guide for Aliens. If the child was adopted, see Adopted child , later.

Thank you for the link, I did already file and so I needed to use it. I am also wondering about previous tax returns that I claimed them,  if I need to amend them? Because we didn't get any of the previous stimulus payments for them. TIA

Everything for the Recovery Rebate Credit will be reconciled on the 2020 tax returns.  The payments in rounds one and/or two were advances on the credit on the 2020 tax return.  

On the tax return you will get everything you are eligible for which is then reduced by any advanced stimulus payments already received.

So on the father's return he will be eligible for himself and two children claimed.  His total eligible amount will be reduced by how much he already received (his stimulus payments).  

On your return you will be eligible for yourself and that is reduced by any payments you received already.

Here is a link for more information on the Recovery Rebate Credit.