How fo I delegitimize incorrect father and establish paternity/collect child support from biological father?

I had my son a few weeks ago and accidentally put the wrong father on the birth cert. & gave him his last name (hyphenated with mine-we are not married). I found out that he is not the biological father and need to get him removed from my son's bith certificate and have my son's last name changed. I also need to establish paternity ASAP to collect child support from the biological father. How do I go about doing so? I know who the biological father is and he is willing to go to an accredited lab to get a paternity test as soon as possible but I'm not sure which lab's tests will hold up in court or could be used for establishing paternity. I also don't know whether or not the man who I put on the birth certificate and whose last name my son has has to be removed before I can collect child support from the biological father. I need to get this done ASAP as I have zero financial support for my son at this time.