Is it permissible for a son to take the remainder of his father's salary without his knowledge, if he fears that his father will not give it to him, especially since his father is going through difficult psychological circumstances?

Taking money from your father without his permission was not permissible, so seek Allah's forgiveness. However, you are not obliged to return it if it was equivalent to your rightful due from him, by way of offsetting. You should also treat him kindly and maintain ties with him in a good manner.