My children are and born in Mexico how do I clam them?

[Hal_Al]

You enter their personal info in the personal info/ dependent section of TurboTax.  Then answer the rest of the qualifying questions. Being a resident of Mexico qualifies for the citizenship rule.  But there are two types of dependents.  Since they don't live with you, you will not get the (up to) $2000 child tax credit. You  only get  the (up to) $500 other dependent credit. 

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit and student status test, a relationship test and a residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. The Other dependent (qualifying relative) credit is worth (up to) $500 per dependent and is non-refundable.  That is, it can only be used to reduce an actual tax liability.

A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:

1. Closely Related OR live with the taxpayer ALL year
2. His/her gross taxable income for the year must be less than $4700 (2023) ($5050 for 2024).
3. The taxpayer must have provided more than 1/2 his support

In either case:

4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse or be claiming a dependent of his own
6. He must not be the qualifying child of another taxpayer

He must have a US social security number or tax identification number (TIN)

[KrisD15]

Enter the child in the Personal Info section of TurboTax and Select A resident of Canada or Mexico from the drop-down list by the Citizen Status input field. 

According to the IRS:

“Child in Canada or Mexico. You may be able to claim your child as a dependent even if the child lives in Canada or Mexico. If the child doesn't live with you, the child doesn't meet the residency test to be your qualifying child. However, the child may still be your qualifying relative. If the persons the child does live with aren't U.S. citizens and have no U.S. gross income, those persons aren't “taxpayers,” so the child isn't the qualifying child of any other taxpayer. If the child isn't the qualifying child of any other taxpayer, the child is your qualifying relative as long as the gross income test and the support test are met.

You can't claim as a dependent a child who lives in a foreign country other than Canada or Mexico, unless the child is a U.S. citizen, U.S. resident alien, or U.S. national.”