Can I consider my children living abroad as dependents in my US tax return? Whats my status?

I am a US permanent resident and my children (below 18) are not, and still living outside US. I am single and not married to my kid's mother, but I totally support them, meaning sending money for their needs. I could not consider my children as qualifying dependents since they dont have SS numbers nor they live with me. How can I avail of any exemption or tax credits in filing my tax returns or maximize my refund? What's my status in filing this return, single or head of household? I have no money for getting tax advise from experts. Please help!