Is it permissible to include the only son as a partner in a third of what the father owns, given that he helps him with the children's needs?

The fundamental principle is equality among children in gifts and endowments, based on the Hadith: "Fear Allah and be just among your children," and His (peace be upon him) saying to Bashir: "Indeed, I do not bear witness to injustice." Therefore, a son helping his sisters does not justify preferring him in endowments, out of concern for aversion.