All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
First of all, we congratulate you for the blessing of embracing Islam. We ask Allah to make you steadfastness upon the Truth until you die.
We advise you to seek beneficial knowledge, perform good deeds, attend circles of Thikr (remembrance of Allah), and keep company with righteous people; these are the best factors that help a person to remain steadfast on the Truth.
As you mentioned, there is a difference of opinion among the jurists about attributing the son born out of Zina (fornication or adultery) to the fornicator or adulterer.
But if that relationship between that man and your mother is considered as marriage in their custom, then he is your father and you are Islamically attributed to him, and his children are your brothers.
Consequently, the ruling of this brotherhood between you and them applies, such as the obligation of keeping ties with them if they are Muslims, and that it is recommended to do so (keeping ties with them) if they are not Muslims, and other rulings.
The same thing applies if he traces you back to him –as it appears from the question –so you are his son, according to the view of some jurists.
Shaykh Ibn 'Uthaymeen was asked about the problem of Zina, which is widespread: “Only few of our brothers and sisters were saved from Zina before they became Muslim. As a result of Zina, many children were produced. With regard to the children who are born as a result of Zina, is it obligatory for their fathers who have become Muslim and who were not married to the mothers to spend on their maintenance?
He replied: “With regard to these people who had intercourse when they were still disbelievers; if they believed that this intercourse occurred in the context of a marriage contract that they thought was valid, even though it is invalid according to the Sharee‘ah, then the children belong to that man. For example, a case of a man who proposed to a woman when he was a disbeliever to be her husband and she agreed, and they thought that this was a marriage contract, and then later the man and woman became Muslim. We say: Your marriage is still valid and there is no need to repeat the marriage contract, and any children that you had are your children [..] With regard to the group of people you mentioned we say: If they believe that their intimate relationships with these women was a marriage, then it is not Zina and the children belong to them. Also, if you believed that it was Zina but you attributed these children to yourself when you were still a disbeliever -- i.e., if the fornicator said: These are my children -- then they are his children, so long as there is no one to dispute with him on this issue (claiming them to be his).” [End of quote]
Since it is proven in the light of what we have mentioned above that you are Islamically his son, then do not pay attention to any whispers, and strive in inviting your relatives to Islam and encourage them to embrace it as Allah may make you a reason for guiding them and you will, therefore, get a great reward.
Sahl ibn Sa’d narrated that the Prophet said to ‘Ali when he sent him to Khaybar: “Go to them patiently and calmly till you enter the land. Then, invite them to Islam, and inform them about what is enjoined upon them, for I swear by Allah, if Allah guides one single man (to Islam) by your efforts, that will be better for you than possessing an abundant number of red camels (a very expensive breed of camels).” [Al-Bukhari and Muslim]
You can make use of the following Fataawa that highlight that Islam is the true religion: 16595, 86091, 88906, 88051, and 82427.
You may also make use of the following Fataawa that show that Christianity is a false religion, and that there are many contradictions in the Gospels, and that they are forged: 8210, 10326, and 90449.
Allah knows best.