As most of us know, in the novels, Bellamy is the son of the Chancellor and Melinda Blake (the show's equivalents are Jaha and Aurora Blake). In both mediums, Bellamy and Octavia are only half-siblings. Now, the show has never hinted at Bellamy and Jaha being related, but if done right, it could be a very good move to have it in S4.
As of S3 finale, Bellamy is on a redemption arc, and Jaha will need a reason to be in the show. Doubtful, but still possible he could be in a leadership position, however, there's also the possibility of the rest of Arkadia disliking him because he brought A.L.I.E. to camp. In any case, Jaha isn't exactly a liked character by the audience. Bellamy has done a redemption arc before, so what could be done to give Jaha a likable trait and a reason to be in the show still, and add a little variety into Bellamy's redemption arc? Make them father and son.
We've seen Aurora Blake in flashbacks, but there's been no appearance (or even a mention, I believe) of either of the Blake children's fathers. Yet instead of just having them as full siblings, they were made half-siblings. To further this, Aurora and Octavia have very light skin, while Bellamy definitely has darker skin. Jaha is black, and biracial children can look white, black, or anywhere between. So it's believable for them to be father and son. Also, Bellamy is 23/24ish, and Wells at the time of his death was 17, and Octavia is 17. In the novels, Jaha had an affair with Melinda, then got married and had Wells. The show could easily do this, or something similar.
However, why even bother? After all, the novels and the show are very different. As said before, both characters could benefit from this. Wells' death affected Jaha horribly in S1, and even into S2, motivating him to find the CoL. If Jaha discovered he had another living son, the show could have it go down two different paths: 1) He could be overjoyed he has a living son and try to build a relationship with him (much more in character and likely) or 2) Since he and Bellamy aren't exactly friends, and he hasn't really been in Bellamy's life for 23/24 years, he could try to keep it a secret but eventually spill it to someone, and it would eventually get to Bellamy. Regardless, this kind of allows Jaha to make a full arc. He was a jerk in S1, no doubt, but he really went on a downward spiral in S2 (desperate to find the CoL to deal with his grief over Wells), which led to him being controlled in S3. Giving him a son with all this going on allows him to redeem himself through the same mechanism that really destroyed him. In any case, this gives the audience a more emotional connection with Jaha and allows us to like him a little more.
It also benefits Bellamy because his only family is Octavia, and we barely saw bits of his mother. So giving him another member of his family, especially one he has less than positive feelings towards, all the while they're trying to figure out how to survive the radiation, would be very interesting and could maybe help Bellamy's character recover from his disastrous S3 arc. Also, if this show decided to kill of Jaha in this season, his death would be much more impactful if he and his son had just barely gotten to know each other as father and son. Especially if Jaha somehow died for Bellamy.