Is it permissible or forbidden for a son to conceal a small portion of his wealth from his father, who has shared all his wealth with him for 13 years and gives his other siblings many times what he gives him, and what is the legitimate Islamic solution to this issue?

Your salary is your own, and you may take from it and give your father whatever you wish. You should be open with your father if you want to take something for yourself, but if that would displease him, you may take it discreetly, provided you leave enough to cover your shared expenses. Financial partnership with him is not obligatory, as each of you has your own money and affairs. You must honor your father, treat him with kindness, and give him what assists him with his life's necessities.