Jotaro is the son of Kenichi and Mariko, but his biological father is Usagi; before leaving to serve Lord Mifune, Usagi had a tryst with his childhood love, Mariko, which led to them conceiving Jotaro. Mariko later discovered she was pregnant. Kenichi, who was also in love with Mariko, convinced her to marry him, so that she would not be dishonored by having a child out of wedlock. Kenichi treated Jotaro as his own child, and genuinely loved as if he were so, but it is one of the many sticking points between Kenichi and Usagi. For his part, Usagi had no idea about fathering a child, and Mariko refused to tell him so as to not make him feel obliged to resign his post and return to her. In Circles, just as Usagi is leaving the village, Mariko tells him the truth about Jotaro, and instructs him not to reveal it to Jotaro, for fear that it would alienate Jotaro from Kenichi.
Later, when Jotaro was old enough to study swordsmanship, he took Usagi's suggestion and came under instruction of Katsuichi-sensei, the same swordsmaster who taught Usagi. He in turn deduced Jotaro's parentage and felt the child was much like his father.
During the third volume of the comic, Jotaro travels with Usagi for a while before Katsuichi is scheduled to meet another swordsmaster named Nakamura Koji for a duel. Before the duel, the four (along with Katsuichi's other student, Shunji) meet in a village besieged by bandits, they form a plan to defeat the bandits and save the town; during which Koji is impressed with Jotaro's skill. When Koji is killed by Katsuichi during their duel, he leaves Jotaro his daisho for him to wield when he comes of age, and the young boy vows that he will grow up to be a great samurai like him; a noble goal according to Katsuichi.
When Jotaro rejoins Katsuichi for more training, Usagi leaves them again. In one of the most touching moments in the series, Jotaro reveals immediately after Usagi's departure that his mother told him the truth about his parentage (but for some reason, she did not tell him that his biological father knows as well). He runs out towards Usagi proclaiming that he is his father; a message that Usagi is too far away to hear.
So far, only a handful of people know the truth about Jotaro and Usagi. Katsuichi knows, likely deducing it from their similar styles, though Jotaro reveals it in front of him in volume 3, issue 75. Usagi has confided their relationship in Tomoe Ame, a possible sign that he thinks of her as more than just a friend.