From: Rabbi Moshe Sofer
To: Rabbi Aharon Segal
On the child support claim, the man must swear he is uncertain the child is his, following the Tashbetz, but only after the child is born. On the esnan claim, a promise to marry cannot be enforced through kinyan, but since the woman's consent was conditional, the man must pay at minimum five gold coins per governmental ordinance, or he may take a shevuas heses denying the promise and be exempt; swearing he never had relations also preempts the child support claim.
Source: Shu"t Chasam Sofer EH II §105