One possible plot could be that Jacob's son discovers his father's past with the werewolves and vampires in the Twilight world. He might struggle to come to terms with his own identity, being part of this complex supernatural world. Maybe he has unique powers that set him apart from the others and has to learn how to control them while also dealing with the politics between the different supernatural groups.
The plot could involve Jacob's son falling in love with a girl from a rival group, like a vampire or a different werewolf pack. This would create a lot of drama as their relationship would be frowned upon by both sides. He would have to fight for their love and also try to bridge the gap between the groups, just like his father once did in some ways.
Perhaps Jacob's son is seen as a sort of prophesied figure. The fanfic could be about how he is expected to bring peace to the long - standing feud between the werewolves and vampires. He might be on a journey to discover the secrets of this prophecy and how he can fulfill it, all while growing up and dealing with the normal teenage problems in the context of this strange Twilight - inspired world.
It could be Renesmee. Since she has a connection with Jacob in the Twilight series, it's not a stretch to think that they might end up having a child together in a fanfic. Their relationship was already quite complex and a child would add another layer of depth to it.
The plot might also involve Jacob trying to keep his child safe from the ongoing feud between the werewolves and the vampires. He could be constantly worried about his child being caught in the crossfire. And as he tries to raise his child, he may also be dealing with his own feelings for Bella or other characters from the Twilight series in a new light.
Well, it could be about Jacob having some sort of physical or emotional burden that makes him 'too heavy' in the context of the Twilight world. Maybe he's carrying the weight of his responsibilities in the werewolf pack, or perhaps he's dealing with a difficult emotional situation like unrequited love for Bella that's weighing him down.
Perhaps in this fanfic, Jacob Black is a big fan of Billie Eilish in his own world. One day, he discovers that her music has the power to break the curse that ties him to his werewolf form. He then embarks on a journey to find Billie Eilish in the human world to ask for her help, facing many challenges along the way, like hiding from vampires who don't want him to be free of the curse.
One key element is the exploration of their relationship. Since they come from different generations and have different outlooks, seeing how they interact and come to understand each other is a big part. For example, Charlie is an older, more practical man, while Jacob is young and part of the supernatural world. Another element is how they fit into the Twilight universe. They both have connections to Bella, and how that affects their relationship with each other is often explored.
In some fanfic settings, they interact as protectors. Jacob is always looking out for Renesmee, being the big, strong werewolf. For example, when Renesmee first goes to school among humans, Jacob might be secretly watching over her to make sure she doesn't expose her true nature.
The other members of the werewolf pack could be important characters. They are Jacob's family in a way, and they would surely be affected by Jacob's state if he's 'too heavy'. For instance, Sam, as the alpha, might try to guide Jacob out of whatever is making him this way.
A third storyline could be them facing threats together. There could be new enemies emerging, perhaps some other supernatural creatures that see Renesmee as a threat or a prize. Jacob and Renesmee would then have to work together, with Jacob using his werewolf strength and Renesmee her unique vampire - human abilities, to protect themselves and their families.
Love is a very common theme. It shows the deep, often instant connection between Jacob and his mate. Another theme is loyalty, as they have to be loyal to each other in the face of various challenges.
I'm not sure specifically as there could be many different interpretations of a 'Twilight' fanfic about the second son. It might focus on a character who is the second son in the Twilight universe, perhaps exploring his relationships, powers, or his role within the vampire or werewolf clans.