Random woman is demanding paternity test from me. What powers do she or I have in this scenario?

As the title says this is a random woman. Not a former sexual partner, not even an acquaintance. But she knows my name and some rudimentary facts about me and is demanding a paternity test saying I’m the father of her child and I’m wondering what to do here?

People are telling me to just do it to get rid of her but I don’t think entertaining the nutcase is a good move. Will she have any legal powers to make me take one? Does she need to have any proof at all that we had sex first before doing so?

Any advice welcome