Even though he doesn't show up much in the autobiography, Franklin's father instills a lot of valuable traits in him and leaves a big impression on him. For example, Josiah teaches his son to value reading and education, even though he can't afford to keep him in school. When Franklin's trying to study and become an author on his own merits, Josiah offers him the (probably) valuable advice that poetry's not really the field for him to go into.
As Franklin gets older, we see him rely on his father directly and indirectly for moral advice. When he's thinking about going into business for himself, for example, it's important to get his father's approval, both morally and financially. Significantly, Josiah supports his son's ideas but says he's not old enough or mature enough yet to run a business properly. He has the good judgment and the strength of will to tell Franklin that, if he returns in a few years with more plans and maturity, he'll help him out with some money then. In other words, he offers his son emotional support even when he's not prepared to become his financial backer.