Living in the Philippines, support mother, a Filipino citizen of our child, an American citizen. Mother has no USA SS number. Can I claim mother as a dependent?

[Vanessa A]

No.  If you are not married and she is not a US Citizen and you are not living in the US, you cannot include her on your tax return at all.

The only benefit to claiming a non-relative on your return is the $500 Other Dependent Credit.  One of the criteria to claiming this is that the dependent must be a US Citizen, national or resident alien.   Therefore, living in the Philippines, she would not qualify.