Rights of child support from a father without marriage

I'm not married to my son's father. He paid child support before the baby was born, and stopped one month before his birth.

What can I do to claim child support from the father for my 9-month old son? He told me I won't be able to do anything because we are not married.

He is from Kenya and I'm from South Africa, and he works for a big company in Abu Dhabi.