I had a baby with a muslim man and we did not get married. He is now involved in her life on occasion; however, none of his family knows about this daughter. What is his responsibility to this child?
As family and the marital relationship are considered as very important and have a high level of what one could call "inviolability" in Islam on the other hand anything which might be considered as contradictory like adultery or any act which may separate spouses are considered as a big crime. Read for example 24:19.
Therefore most (if not all) Muslim scholars in case of zina even don't allow a marriage if it is clear that the women is pregnant. A kid from such a relationship would never be attributed to its father based on ahadith like this (from sahih al-Bukhari, which can be found in other hadith compilations)
"The boy is for (the owner of) the bed and the stone is for the person who commits illegal sexual intercourse.'
Which is interpreted that a (legal) child would get the name of the husband while a illegal child won't as in first place those who commit zina should be punished!
This is why the father according the shari'a wouldn't have any responsibilities or duties towards this child. But he must be aware that he will face his Creator and would be taken into responsibility. And if he had something like a conscience he should care for his child if he knows it is his!
Note that a woman also has no duties (unless she has no husband) expect taking care of a child according to shari'a, as feeding and clothing is (or should be) the duty of a husband. Even if this is not a duty a woman or mother would never leave her child, so caring for her child would let her gain rewards from Allah if she did it the best way.
This means that from a legal point of view doors seem to be closed (at least as far as I understand or found). I even found a fatwa neglecting the fact of the DNA proof. This for sure is something irritating for us nowadays!
The fatwa with the corrupt English-link i added as an Arabic source quotes from a hanafi book the following fatwa:
جاء في " الفتاوى الهندية " في فقه الحنفية : " ولو زنى بامرأة فحملت ثم تزوجها فولدت ، إن جاءت به لستة أشهر فصاعداً ثبت نسبه منه ، وإن جاءت به لأقل من ستة أشهر لم يثبت نسبه إلا أن يدعيه - أي يدعي أن هذا الولد ابنه - ولم يقل أنه من الزنى ، أما إن قال إنه مني من الزنى فلا يثبت نسبه ولا يرث منه "
--- (my own translation take it with care) ---
In the book "al-Fatawa al-Hindya" (the Indian fatwas) from the hanafi school of fiqh it is said: If a man committed zina with a woman and she became pregnant and they got married and she gave birth, if the child was born during 6 months or more the attribution to the husband is considered as given, but if she gave birth in less than six months than the attribution to him is not assured unless he claims this - means he claims that this child is of his own- and he didn't say that it is a child of zina, but if he said it's a child of zina the attribution to him is not considered as given.
But there's an option that good people should take care of such a child as it is sinless in the sinful act which happened between the biological parents and it is haram to insult such a child for the parents sin!
Or the biological parents get married and take care of their child, especially if they both know they are the parents, that they sinned and repented unfortunately this is more an opinion based part of the answer!
Of course if this doesn't work and you live in a non-Muslim country you are free to relay on the state law, if the biological father is not caring for his child as he should.
I am a muslim, but I strongly object to the interpretation/assessment given here in terms of responsibility of the father towards a child out of wedlock.
Islam is a religion of nature, meaning anything that sounds unnatural and contrary to common sense cant be islamic. The idea that that father of the child has no responsibilities is absurd and unacceptable ! I do not have relevant ahdadith etc but I advise the mother and the readers to not take this assessment as correct.
It is only 'one' interpretation of the hadith. And I firmly believe it has has not taken the context and other aspects in account.
I think the hadith in question implies that the parents would be punished as per law if for sex outside marriage, but the child is from the bed means, the parents are the ones who were on the bed.
So, the mother and father of the child are the ones who conceived him on that bed. Meaning that whether or not they were married does not change the fact that the child is theirs and they have all the obligations to fulfil towards that child irrespective of their marital status.
THAT in my opinion is what child is from the bed means, in contrast to saying 'child is from the wedding/nikkah' Allah knows best but in my opinion this is the natural and logical common sense meaning of the hadith. Why would islam punish the child by taking from him/her the right to having his father's name and care.