My cousin got pregnant in July 2011 and is trying to pass it off as one guys child. But upon speaking with one of my close friends (her ex) they had unprotected sex around the time of conception. The child looks nothing like the other father but looks just like my close friend. How can he go about getting a paternity test because he loves this little girl and he has already missed so much time with her. We all reside in Cuyahoga County, Ohio if this helps. Also, he suspected the child was his but didn't step up right away because she only wants him as a friend and is currently pregnant by the other guy "again"

He files to establish paternity and move for parenting time.

Who is on the birth certificate? Was she married to this other guy when the baby your friend thinks is his was born?
His reasons for nonpayment of support are shaky, however, if he is not on the birth certificate and has not been found the father he has no legal obligation to support the child.

But he should bear in mind that if he is found to be the bio dad (which may or may not be likely... she may have had relations with both men around her ovulation) the state will be going for child support if the mother of the child is getting state assistance.

As noted, he files in Family Court for custody and visitation. The court will order a paternity test be done.

I would strongly advise getting an attorney to do this. I believe OH law allows for a paternity challenge until the child is 18.

Also, he files in Juvenile Court rather than Family Court, unless I am incorrect, because I am assuming he was not married to the mother of the child at the time of her birth...
Correct me if I am wrong, but that was my experience in Ohio in a county close to Cuyahoga.

In some counties, Juvenile court is under the umbrella of family court. In others it refers to a court that does criminal prosecution of minors. If the OP asks for family court he will be directed to the proper court.