If I were you, stop contacting the parents.
Why?
It could cause legal trouble for your son.
How?
The girl is a minor.
Need I say more?
Just leave the girl and her family alone, and advise your son to do so, too.
There will be a better time to address this matter.
Stop POKING the bear, for your son's sake.....
Yes, an unmarried male PROVEN to be the putative father of a child can be held accountable to pay child support.
However, if he has no income, the child support would be a minimum amount.
In Ohio for one child, the charted child support amount is about $6,500 per year.
If the putative father is ordered to pay support, he must pay $4,875 per year, or 75% of the charted amount, if he earned 75% of total combined parental income.
It is complicated and my numbers are only meant to illustrative of a fictional scenario.
If your son will be attending high school, his income will be nil or minimum wage.
If he elects to matriculate to college, he might have little or no earned income for four years.
The child support meter will still be ticking and a debt accruing.
You should suggest to your son to have a paternity test done prior to going TOO far down this slippery slope.
If he isn't the father biologically, it is best that he know it NOW rather than in five years.
How child support is calculated in Ohio:
ODJFS Online | Office of Child Support
https://support.franklincountyohio.gov/CSEA-website/media/Documents/Fact Sheets/ocda-faq-guidelines_Franklin-bookletPDF.pdf
Ohio Child Support Chart
How is Child Support Calculated in Ohio? Use our Calculator
One final note for the moment.
You and your son should consult a family law attorney so that he (and you) can learn just what the law requires of unmarried males who father children.
There will be visitation for your son, eventually, once he has proven his paternity.
For the next three or four years, he can forget custody, if he is the putative father.
That is why a consultation with a family law attorney near you would be useful.
Normally the initial consultation is offered gratis.