Is there a statue of limitations for getting a paternity test?
This is the situation:

Joe has sex with married woman.
Married woman gets pregnant.
Husband knows baby could be Joes.
Husband signs birth certificate.
No paternity is established.
Husband says that the baby is his.
Joe does not care.
Joe doesn't want married woman.
Joe doesn't want a baby.
Married woman constantly threatening to leave husband.
Married woman constantly threatening Joe with child support.
Its been 3 years of this for Joe.

It will depend by state, depend is married women listed husband as father. In some states there would be no allowance for DNA tests because she was married, if she claims it is husband, in otherr states there is no time limit until child is 18.

So basically wihtout knowing your state not much to tell