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.
The correct course of action is not to inform about the previous affairs that your father had, because it is Islamically required to conceal the sins of the Muslim.
Abu Hurayrah narrated that the Prophet said: “Whoever conceals the sins of a Muslim, Allah will conceal his sins in this life and on the Day of Judgment.” [Al-Bukhaari and Muslim]
If your father had this child outside marriage wedlock, then it is not his child and he/she is not to be traced back to him, according to the opinion of the majority of the jurists. Rather, the child is traced back to his/her mother, as already discussed in Fatwa 85430.
However, if your father accepted to have the child be traced back to him - as it appears – and the mother of the child did not give birth to him/her while she was married, then, in this case, the child can be traced back to your father according to the view of some scholars, and this is the view chosen by Ibn Taymiyyah and Ibn Al-Qayyim .
Based on this, this child will be your half sibling and has the rights and obligations of brotherhood/sisterhood.
In this case, that family had to inform you about this relationship while concealing the sin of your father in that relationship so that two benefits will be combined together.
This is based on the assumption that this relationship was not legitimate. However, if it was a legitimate relationship and the woman was his wife, then you do not have to tell your mother about it. The fact that a man has a previous wife is not a shame so that one would inform the people about it.
If it was his wife, then this child is definitely your half sibling and that family should have informed you about it and not hide the matter as we have already mentioned because of the considerable Islamic benefits in that.
For more benefit, please refer to Fatwa 370801.
Allah knows best.