I have found out in the last few years that I "might" have a daughter. A woman I was dating in 1992 told me a few years ago after I had asked if her daughter was mine said "You don't have any kids with me, but if you did, she's calling Mike dad now!" She has never given me a definite answer as to whether I am the biological father of this young girl or not. Does anyone know if I have any rights to find out for sure? Whether, I would still like to know.

I will tell you one thing, that if there is a support order, it is your responsibility to challenge paternity. There is a statute of limitations in most states, and if you miss it, you could still pay support on a child that isn't yours.

The laws are in favor of women. A woman can have a kid, point to a man on the street and say, "HE is my baby daddy", and the state will go after him. If he wants a paternity test, then he has to pay for it. Many men are having to pay support on kids that aren't theirs when they were married to a woman who cheated on them, and they were railroaded by antiquated laws favoring the woman.

This is bad for the man having to pay, and it also denies the bio dad the right to support his child.

If you wanted a relationship with this child, maybe you could demand a paternity test? You don't want this woman coming after you later saying, "You own me $50,000 in back child support payments". She sounds a little nuts.

It depends on the state, if she was married when the child was born, that differs. In many or even most states yes you can file for a paternity test, expect to pay for them. If the child is yours, then you can file for visitation and have child support set. But as noted, and I am sorry to say this, you would have all of those years of back chlid support she could come after.
So considering the child is now 16, I don't know if it is really a good idea, hard for me to say that, but she will never think of you as dad, and if as a adult latter she wants to know, she can come and the two of you be tested.

Who is listed as the father on the birth certificate? If you have good reason to believe you are the father then you can file a motion with the Family Court in your county for an adjudication of paternity. Keep in mind that, if you are proven to be the father, you could be held responsible for $1000s in back child support.

Let sleeping dogs lie, my friend because it will be a lot of courts, lawyers and hassles. You may have a right to petition for a DNA test, but will it be worth the disruption of all the peoples lives, that are involved. Take her word and stay out of it. Give this child a break after 15 years.