Firstly: 

We ask Allaah to pardon us and you, and to help us to repent properly and turn to Him, and to bless us with good and righteous offspring by His grace and bounty. 

Remember that repentance and guidance are the best things that a person may be blessed with in this world; they are the greatest blessings that Allaah can bestow upon us. So we must be grateful to Allaah for them, and strive to renew them. The Prophet (peace and blessings of Allaah be upon him) used to pray to Allaah for forgiveness and repent to him one hundred times every day, as was narrated by Muslim (2702). 

Secondly: 

With regard to the attribution of illegitimate children, the fuqaha’ have discussed this issue in detail and they said that one of two scenarios must apply to the woman with whom zina is committed: 

1 – Either she is married, in which case any child who is born to her is to be attributed to the husband and not to anyone else, even if she is certain that he is the child of the one with whom she committed zina, unless the husband disowns the child by means of li’aan, in which case the child is not attributed to the husband, rather he is to be attributed to his mother and not to the zaani (adulterer). 

2 – Or she is not married. If an unmarried woman has a child, the scholars differed as to whether the child should be attributed to his father, the zaani, or to his mother. There are two opinions, which have been discussed and the evidence for them quoted, in the answer to question no. 33591. See also the answers to questions no. 117, 2103 and 3625. There it says that the correct view is that this attribution is not valid, so it is not permissible to attribute the illegitimate child to the zaani, rather he should be attributed to his mother, even if there is certainty that this child was fathered by this zaani. 

It says in Fataawa al-Lajnah al-Daa’imah (20/387): 

The correct scholarly view is that the child is not to be attributed to the man who had intercourse with the woman, unless intercourse took place within the framework of a valid or invalid marriage or something that may be taken as a marriage contract or concubinage or something that may be taken as concubinage. In such cases, the child may be attributed to the man who had intercourse with the woman, and they may inherit from one another. But if it was a case of zina then the child cannot be attributed to the zaani. Based on that, he cannot inherit from him. End quote. 

It also says in Fataawa al-Lajnah al-Daa’imah (22/34): 

With regard to the illegitimate child, he is to be attributed to his mother, and he comes under the same rulings as any other Muslim if his mother is a Muslim. He is not to be blamed or put to shame for his mother’s crime or the crime of the one who committed zina with her, because Allaah says (interpretation of the meaning): 

“And no bearer of burdens shall bear another’s burden”

[Faatir 35:18]

End quote. 

Thirdly: 

It is well known that attribution of lineage affects many rulings such as rulings on breastfeeding, custody, guardianship, maintenance, inheritance, qasaas, the hadd punishment for stealing, slander, testimony etc. Because the more correct view is that the illegitimate child cannot be attributed to the zaani, none of the rulings mentioned above can be proven to apply to the father of the illegitimate child, rather many of them apply to the mother. 

But the illegitimate father (the zaani) is still affected by the rulings forbidding marriage. According to the majority of scholars, the rulings forbidding marriage still apply between the illegitimate child and his father and his father’s relatives. 

Ibn Qudaamah (may Allaah have mercy on him) said: 

It is haraam for a man to marry his illegitimate daughter, or his illegitimate sister, or his (illegitimate) son’s daughter, or his daughter’s daughter, or his brother’s daughter, or his sister who is illegitimate. This is the view of most of the fuqaha’. End quote. 

Al-Mughni (7/485). 

Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) was asked about an illegitimate daughter –can she marry her father? 

He replied:  

Praise be to Allaah. The view of the majority of scholars is that it is not permissible to marry her. This is definitely the correct view. End quote. 

Majmoo’ al-Fataawa (32/134). 

It says in al-Mawsoo’ah al-Fiqhiyyah (36/210): 

It is haraam for a man to marry his illegitimate daughter, because of the clear meaning of the verse (interpretation of the meaning): 

“Forbidden to you (for marriage) are: your mothers, your daughters…”

[al-Nisa’ 4:23]

because she is his daughter in a real sense and in linguistic terms and she was created from his water (i.e. sperm), so the illegitimate son is forbidden (in marriage) to his mother. 

This is the view of the Hanafis and of the Maalikis and Hanbalis. End quote. 

Fourthly: 

Based on the above, it is not permissible for this illegitimate son of yours to marry your daughters, so they are his like sisters. The same applies to your wife. 

But that does not mean that he is a mahram for them in the sense that they may be alone with him and take off their hijab in his presence. Prohibition of marriage does not always mean that one is a mahram in the sense that it is permissible to be alone with the person etc. This is an additional ruling which applies only to the shar’i mahrams, so attention must be paid to that. 

Ibn Qudaamah (may Allaah have mercy on him) said: 

Zina means that a person is forbidden in marriage, but it does not make the person a mahram or make it permissible to look (at a member of the opposite sex). End quote. 

Al-Mughni (7/482). 

This does not mean that you should not treat this young man kindly and strive to bring him to Islam and make him a member of the family, but he should not be attributed to his illegitimate father, and the issue of the daughters of the family observing hijab in front of him should not be taken lightly. We ask Allaah to bless you and guide you. 

And Allaah knows best.