Can't happen unless there's some step-relationship here, such as a man marrying his step-mother, the wife of his father. That still makes you your father's son in any case, but now you have become...
Whether "your father and I" or "your father and me" is the correct construction depends entirely on how it is used in the sentence. "Your father and I" would be correct only where the use of "I"...
Jacob, father of Joseph (Matthew's Gospel), was the son of Matthan, son of Eleazar.Heli, father of Joseph (Luke's Gospel), was the son of Matthai, son of Levi.