Is the questioner entitled to claim half of the dwelling that he contributed to building?

If the son worked with his father for a period without compensation, he has the right to demand the wage of similar work (ajr al-mithl), unless he gratuitously relinquished it or there is a recognized custom that he is not entitled to it. This should be determined by experts. He is not entitled to any part of the house in return for that, unless there was an agreement.

If the son completed the construction of the house with his own money without an agreement on a share in the house, then this money is a debt owed by the father, and the son does not have the right to claim sole ownership of any part of the house.