Can claim my daughter, 10 years old, living out of the country with no SSN as a dependant when filling taxes?

No.   In order to claim a child as a dependent the child needs a SSN or an ITIN.

No.  In order to claim anyone on your return, they at minimum have to have an ITIN.  

 

Also, who is supporting her?  Do you pay over half of her support?  If so, it is possible that if she had an ITIN you would be able to claim her for the $500 Non-Refundable Other Dependent Credit

 

Claiming Non Citizen Spouse and Children on Your Taxes

 

How to obtain an ITIN

Not unless she lives with you and you provide more than 50% of her support

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