Is genetic testing required for me to be able to get child support for my child, who is about to start school next year, if his biological father , a foreigner living overseas, was not registered on the birth certificate?

Yes - most probably! The Ministry of Interior will  probably refuse to register the father on the basis of declaration that is made several years' late, or other cirucmstantial evidence, that is available and you will be required to file for a declaratory judgment of  paternity at the family court ( jointly, if the presumed biological father is co-operative).

Depending on the circumstances, it might be possible to persuade the court to make a declaration of paternity on the basis of evidence and order the Ministry of Interior to register paternity, although is is likely that the court  will only do this after DNA testing is carried out and there is  a positive finding of paternity. 

Once paternity is established, an applicaiton for child support can be filed against the biological father or an agreement can be reached between you and him, which can be authorized at the family court, and become legally binding.