Now lemme put a disclaimer. I’m not a big fan of canon/canon children. I especially am not a big fan of ZeLink. But I just got this stupid idea stuck in my head for a character in the BotW era thanks to seeing other kids of the same pairing. Honestly they tend to be characters that follow in Link’s footsteps and refuse to be royals. A select few are just ROYALS. I kinda wanted to try to do something different and look at this pairing in a respect that would influence both parental characters and their child. If that makes a lick of sense. But here I go!
Now it’s a view of mine that Link’s amnesia means he’s not quite the same person that he was before. Most of the memories obtained don’t really involve him that much (IE we see things he would have never see) or are only a tidbit. He does learn about who he was but this is pretty much a person who finds he doesn’t like who he was given how the world is now. He’s happy to be exploring but there is an obligation to Zelda given everything that his past friends have told him. There is a regret and such towards losing them and not really being able to be with them to completely rediscover who he was. Still he slays Calamity Ganon as he was told, rescues Zelda, and feels obligated to try to stay with her to learn more about himself.
What am I getting at? In short, despite Link’s liking of how he is now, he still feels that he owes Zelda for failing in the past despite not remembering everything. He wants to make sure she can be happy like he is and intends to repay her for what she lost. Thus why he decides to go with her. In return, Zelda’s feelings do grow towards him. The relationship is one sided. Link’s feelings are that of obligation while Zelda’s are love. Link understands that the castle (and Hyrule itself) won’t be rebuilt in his lifetime and still wants to explore lands beyond this one. Zelda refuses to leave and feels a tad betrayed by Link. At the same time though, she is somewhat understanding of why. Needless to say this awkward relationship did end up with a child.
The little boy (whom I will call Joe because Bernard still belongs to Alden >C) does have both parents for a while. Link feels obligated to stay given child. Link loves his son as does Zelda. However Zelda is very much reset on rebuilding Hyrule with the Zora’s help. The Zora are very helpful in convincing others that Zelda is the princess of Hyrule and that things are getting better. So rebuilding is ensuing. This means that Link spends more time with the boy than Zelda, not that she means to be neglectful. Link also is placed with the responsibility to try and rebuild some sort of knight/army things which is very neglectful of doing if not for his laziness and attention to his son. Joe very much is a daddy’s boy compared to mommy’s. And this becomes an issue.
Around Joe’s 8th or so birthday, Link is pretty fed up with how Zelda is more interested in rebuilding Hyrule than her actual family. He tries to bring up how they should just forget this whole ruling thing and go back to how things were before they had a child. Zelda is stuck on rebuilding to try and ensure Hyrule’s safety and their son’s, which she’s offended that Link would forget that. She’s missing the point that her son has been treated much like her father treated her (a point Link brings up) before Link decides to leave with their child. No one dares stop Link from leaving.
For a few years Joe and Link live together. Joe isn’t very fond of living off the land and wants to go back to the little house they had outside the destroyed castle. Link isn’t against this for his son however he knows he can’t go back. It’s kind of a tear situation as he doesn’t know what to do for Joe. Meanwhile Joe’s learned a little about how his father really feels towards the past and the little guilt he has for abandoning Zelda. Comparing it to champions he’s only heard songs of and the picture of these individuals he’s seen. Despite Link’s desire, he does ask Joe if he wants to stay with his mother. Since the answer was a yes, Joe is returned before Link goes on his way where he won’t see either of them for a long time. The only thing really stated is that the winds will help Joe find him if he needs to.
From there, Joe gets back on track to a more ‘royal’ trained lifestyle. This isn’t something he really enjoys either. Despite the dislike for the wild lifestyle, he still would rather not have all these things hanging on him and his mother pretty much ignoring him most of the time. For a good time he does feel alone. And one lucky night, he is able to catch Zelda and talk to her about this. She only had a feeling about it but didn’t know what to do. She states she doesn’t know how to be a proper mother before talking about her own and Urbosa. Joe brings up a bit about Link, turning Zelda a little bitter before admitting she was being a tad selfish asking him to get rid of his own happiness.
Joe at this point realizes that the time their parent’s come from (100+ years ago now) was much different and they both have issues. From here, he makes a mature reasoning that they’re both never really going to get what they really want. Both want to ensure that this never happens again despite the different roads taken. The only way to ensure it is to try to reach a middle which will probably never happen. Joe decides that this will be what he will do to help bring peace to Hyrule and his family.
Into his late teens, Joe tries very hard to balance a life of learning to live in the wild and take royal duties. Ideas that he comes up with are shared with his mother which sometimes are implemented into the rebuilding Hyrule. In doing this, he learns that he isn’t very much like his father or his mother. He doesn’t necessarily have the intelligence that Zelda has and he’s a poor combatant (and a coward) compared to Link. The only thing he has going for him is his diplomacy skills between both. Talking to people is something he’s enjoying and a great way to learn the lands. All the races have a rich history and together they build something strong. For once he sees more of Zelda’s side than Link’s. Getting this history gathered is what he decides to do when he becomes an adult.
Leaving Zelda to ‘rule’ and look over the rebuilding of Hyrule, Joe leaves the somewhat rebuilt Castle Town and Castle in order to ensure that the library’s pages can grow. The hundred years of malice had ruined so much of the library that he wishes to restore it. And his desire to try and find some understanding of his parent’s issues through history is also a big part. Despite only going with his appointed knight and a guide that changes every so often, Joe is very much treated like a prince despite him trying to help where he can.
Personality wise, Joe is a rather peaceful individual and he doesn’t much care for conflict. It upsets him easily as he had seen enough of his parent’s bickering when he was little. As an adult, he can deal with it more but he is prone to shouting to make people stop. He tries his best to be more of a prince but there is a little allure to breaking the rules much to his mother’s dismay. He is seen as a strong diplomat and a great historian of the land. He has spent many hours trying to recollect the lost history of Hyrule and its races while being the best diplomat he can. His appointed knight sees him get into situations that he cannot handle for the sake of writing down history and often has to save him. Joe does get a thrill from dangerous situations but also knows if it wasn’t for his knight, he would be long gone. This doesn’t mean that he hasn’t had a good time hunting or has been able to take down some weaker monsters from afar with a bow. Still he’d much rather talk with the monsters in some way (as he has tried to do many times with little to no results from larger monsters) and bring a peace to them as well. As such, there is even history being started on monsters thanks to him. In terms of more of who he’s like however, he’s more like Zelda despite him saying he’s more like his father. He uses what she has taught him most though Link’s ingenuity does help quite a bit.
When Joe is eventually an adult, he resembles King Rhoam very much. The big nose, the bulky build (which I’m guessing beyond the layers of clothes Rhoam wears, he was once a pretty decently built guy at one point if not a fat king eventually later), and the more curly hair. Still he has his parent’s eyes and his grandmother’s hair color (which let’s just be crazy and say it was... a shade of brown XD or red blonde OR SOMETHING not freaking BLONDE) though he keeps it short unlike his parents. His appearance alone brings a commanding presence to where he goes as his voice carries it as well.
The real question though is if he ever runs into his father ever again? The answer is yes. He has been able to find his father around Hyrule on his journeys. Link’s insight of what he has learned in his travels are often translated as father/son time into books that can be put into the library. Link even offered up the picture of the Champions as a gift to Zelda and the Library.