[MENTION=16760]xboxisdead[/MENTION]:
Punishment of fornication isn't easily applied
https://islamqa.org/hanafi/daruliftaa/7741?_e_pi_=7,PAGE_ID10,2074668781
According to fatwa you are discussing the child will be attributed to the person whoever does a pregnant woman marry with, but if the child is born prior to 6 month, it goes to mother and in case of a single mother as well but as far as financial burden on fornicator is concerned that fatwa is silent.
however, what punishment or responsibility of fornicator regarding the woman and the child is concerned the judge in an Islamic state take the decision by doing ijtihad in case Adilla e shariah is silent regarding it. Because in an Islamic state the woman isn't supposed to go for job then who will give financial support to woman or bear the expenses of a woman and her child, is to be decided by the judge.
Indeed, the male fornicator is deprived of the right of paternity, but he can't be allowed to be scotfree. All the pros and cons of the case will have to be taken into consideration by the judge and he will take the decision accordingly.
Since this matter is between a Christian and a Muslim which seems to be an unprecedented case the decision to settle it entirely depends on discretion of the judge.