Is it impermissible or permissible for a father to prevent his youngest son from being given a quarter of the house, knowing that the eldest son owns a quarter of the house from his own money and provides for his parents and family, while the youngest son does not contribute to expenses and his father favors him over the eldest?

If a father registers a house in the name of one son to the exclusion of others, this act is forbidden and unjust, and the Messenger of Allah (peace and blessings of Allah be upon him) forbade it. It was narrated from Nu'man ibn Bashir that the Prophet (peace and blessings of Allah be upon him) said to his father when he wanted to bestow a gift upon his son to the exclusion of his siblings: "Have you given all your children the same?" He said: "No." He said: "Then take it back," and in another narration: "Indeed, I do not bear witness to injustice." Therefore, the father must refrain from doing so, and the questioner should try to dissuade him in a good manner.