Can you get child support if the father is a citizen of another country?

If you have custody of the child(ren), and if the father lives in the US, then yes, you can get child support even if he's not a US citizen. If he was ordered by the courts to pay child support and refuses to pay, you can sue him for non payment. They may even order (or you can request) the child support payments to go through the Child Support Enforcement Agency, who will then forward the payments to you. If he fails to pay, then they will take legal action on your behalf.

But if he lives in another country, then it may be extremely difficult, if not impossible, to force him to pay the child support unless he lives in a country which signed the Hague Treaty, which provides enforcement for foreigners to pay child support.