A Muslim whose kaafir family are threatening to hang him because of his being Muslim

First of all I would like to give you the glad tidings of the words of the Prophet (peace and blessings of Allaah be upon him): “There will come a time when the person who is patient in adhering to his religion will be like one who holds on to a life coal.” Narrated by al-Tirmidhi from Anas; classed as saheeh by al-Albaani because of corroborating reports. See al-Silsilah al-Saheehah, 957 

We ask Allaah to make you steadfast in adhering to the truth and not to let the blame of anyone or the evil of any wrongdoer affect you. Remember the words of Allaah to His Prophet (peace and blessings of Allaah be upon him): 

“but beware of them lest they turn you (O Muhammad) far away from some of that which Allaah has sent down to you”

[al-Maa’idah 5:49 – interpretation of the meaning]

I advise you to flee for the sake of your religion to a place where you can find people to help you follow the truth. Allaah says (interpretation of the meaning): 

“He who emigrates (from his home) in the Cause of Allaah, will find on earth many dwelling places and plenty to live by. And whosoever leaves his home as an emigrant unto Allaah and His Messenger, and death overtakes him, his reward is then surely, incumbent upon Allaah. And Allaah is Ever Oft‑Forgiving, Most Merciful”

[al-Nisa’ 4:100]

At the same time, you should pray for your family and ask Allaah to guide them and open their hearts to Islam. 

Finally, I ask Allaah to make the Muslims happy by supporting Islam and helping the believers and humiliating the kaafirs. May Allaah guide your family to Islam.