All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If this man is religious and has a good moral conduct and you both want to marry each other, then you should accept to marry him. What you mentioned about him doubting his son not to be from him should not be a hindrance for you to complete this marriage. However, we advise you to perform Istikhaarah prayer about him so that Allaah would choose for you what is best. For more benefit on how to perform the Istikhaarah prayer, please refer to Fatwa 81434.
As regards this child, if that woman gave birth to him while she is the wife of that man during a period in which this child could be from him, which is the minimum period of pregnancy (i.e. 6 months), then the child is Islamically traced back to him. The only way for this child not to be traced back to him is if he [the husband] denies him [the child] by invoking Li’aan (i.e. he and his wife invoke the curse of Allaah on the liar among them when he accuses her of having committed adultery]); for more benefit, please refer to Fatwa 84301.
If it is confirmed that the child is his son as he is the owner of the bed (i.e. the legitimate husband of this woman), then no consideration should be given to the DNA test because the Sharee’ah takes utmost precautions to trace back the child to his father; so it traces back the child to his father for the least possibility. For more details, refer to Fatwa 122944.
Besides, it is not permissible for a person to deny his paternity of his son just because he does not resemble him; who knows, it might be that he resembles his grandfathers. The evidence for this is that Abu Hurayrah narrated that a man came to the Prophet and said: “O Prophet of Allaah! A black child has been born for me.” The Prophet asked him, “Have you got camels?” The man said, “Yes.” The Prophet asked him, “What color are they?” The man replied, “Red.” The Prophet said, “Is there a grey one amongst them?” The man replied, “Yes.” The Prophet said, “Whence comes that?” He said, “May be it is because of heredity.” The Prophet said, “May be your latest son has this color because of heredity.” [Al-Bukhari]
An-Nawawi said: “The son is traced back to the father even if his color is different from that of his father.”
On the other hand, if divorce takes place, it is permissible for that man to discuss with that woman (his ex-wife) the affairs of their son, because it is permissible for a man to speak to a non-Mahram woman for a need if the religious conditions are met, like not being in seclusion with her and the like. For more benefit, please refer to Fatwa 128779.
Finally, it should be noted that separation between the husband and his wife in itself does not lead to divorce; rather, the bond of marriage still exists even if the period of separation is long unless the husband divorces her or that an Islamic judge divorces her from him. Similarly, if a husband initiates divorce, then divorces takes place and the wife observes a waiting period and this has nothing to do with authenticating the divorce in the court. In addition to this, it is not permissible to resort to non-Islamic courts except in case of necessity. Moreover, the divorce that is issued by such courts is not valid unless the husband initiated divorce as per the Fatwa of the Assembly of Muslim Jurists in America. In this case, the husband should be careful about any legal accountability regarding this.
Allaah Knows best.