If someone has not been served with court papers regarding a paternity suit that has been filed against them but has received a letter in the mail informing them of the hearing date, time, and location what will happen if you do not show up?
Nothing. You have to be SERVED.
Unless you signed a WAIVER (I assume that you weren't).
Or: unless you MADE AN APPEARANCE by filing an answer or other pleading in the case.
If none of those things happened: You don't have to go to Court, and nothing will happen.