Deductions & credits

As long as you and your child meet the other qualifications (see extract below), you could claim a child tax credit.  Not having a home in the US determines if the credit if fully refundable or not.  Here is an IRS FAQ with more information.

Since you did not have a main home in the US for at least 1/2 the year, your child tax credit is not fully refundable.  The maximum child tax credit is either $3600 (child age 6 or under) or $3000 (over age 6 to age 17) but that amount is further limited by your tax liability.  If your tax liability is zero then your non-refundable credit will be zero for example.

There is also a refundable additional child tax credit.  However, when your Child Tax Credit is more than your tax liability, your ability to claim any Additional Child Tax Credit more than your tax liability is limited in two ways.

• You must have earned income in 2021. The Additional Child Tax Credit increases when your earned income is higher.
• The Additional Child Tax Credit cannot be more than $1,400 per qualifying child.

TurboTax will calculate these credits based on your entries.

If you have child under age 18 who has a valid social security number and is a US citizen and meets the criteria below you would be eligible for the Child Tax Credit.

1. The individual is the taxpayer’s son, daughter, stepchild, eligible foster child, brother, sister, stepbrother, stepsister, half-brother, or half-sister, or a descendant of any of them (for example, a grandchild, niece, or nephew).
2. The individual did not provide more than one-half of his or her own support during 2021.
3. The individual lived with the taxpayer for more than one-half of tax year 2021. For exceptions to this requirement, see Residency Test in IRS Publication 501, Dependents, Standard Deduction, and Filing Information.
4. The individual is properly claimed as the taxpayer’s dependent. For more information about how to properly claim an individual as a dependent, see IRS Publication 501, Dependents, Standard Deduction, and Filing Information PDF.
5. The individual does not file a joint return with the individual’s spouse for tax year 2021 or files it only to claim a refund of withheld income tax or estimated tax paid.
6. The individual was a U.S. citizen, U.S. national, or U.S. resident alien. For more information on this condition, see IRS Publication 519, U.S. Tax Guide for Aliens PDF.

Next,  you would choose the Foreign Tax Credit over the Foreign Income Exclusion when you live in a high tax area.  The top tax rate in the US is 37%.  So if the tax rate in India is over that then the tax credit would be beneficial.  The best way to know for sure is to try both ways to see which is more beneficial in your situation.