Their relationship could be portrayed as more of a brotherly bond. Goku could be like an older brother to Gohan, showing him the ropes of being a Saiyan and having fun adventures together.
It could also be shown as a mentor - student relationship where Goku is very strict in teaching Gohan everything he knows about fighting and survival. He might push Gohan harder than in the original series, which could lead to some interesting character development for Gohan.
One way is to make Bardock a sort of guardian angel figure for Baby Goku. He's not physically there but can influence Goku's life in small ways. For example, he might cause a gust of wind to push Goku in the right direction when he's lost in the forest as a baby. Also, their relationship could be explored by having Bardock's old enemies mistake Baby Goku for Bardock and target him, and then through these encounters, we learn more about how Bardock and Goku are related.
In many fanfictions, Goku's protectiveness of Gohan is shown through his constant presence. He might train Gohan more rigorously to make him stronger so he can defend himself. For example, in some stories, Goku takes Gohan to special training grounds that are hidden from the rest of the world. This not only protects Gohan from potential threats during the training but also hones his skills in a more secluded environment.
Their relationship can be portrayed as a father - son dynamic. Instead of the usual enmity, Vlad could be a strict but loving father figure to baby Danny. He might scold Danny when he does something wrong with his powers, but also be there to comfort him when he's scared.
In some fanfictions, Gohan and Goku might have a series of conversations that open up new levels of understanding between them. Gohan could share his thoughts and feelings about his life and future, and Goku would listen and offer his own insights. This kind of communication can really strengthen their bond.
In a Gohan x Goku fanfic, their relationship can be delved into by creating scenarios where they have to rely on each other completely. For example, if they are in a situation where Goku's strength and Gohan's intelligence are both required to escape. Their different personalities can also be highlighted. Goku's carefree nature contrasted with Gohan's more studious and responsible side. And of course, flashbacks to Gohan's childhood and how Goku's presence or absence affected him can add depth to their relationship.
Their relationship could be portrayed as a mentor - mentee relationship in a different way. Instead of Orochimaru trying to use Naruto for his own gain, he could genuinely see Naruto's potential and guide him in the ways of some of the more esoteric jutsu. For example, Orochimaru could teach Naruto about the secrets of the snake contract without any ulterior motives. Another way is to show them as reluctant allies. Maybe there's a common enemy that is so powerful that they have no choice but to work together, and over time, they start to respect each other's abilities.
They could be shown as more protective. Shepard, who was already a strong and brave character, becomes even more vigilant to keep his family safe. Liara, on the other hand, might be more nurturing and use her knowledge and wisdom to raise the baby in a way that combines both asari and human values.
In some fanfictions, the Naruto - Sakura relationship is portrayed as a slow - burn romance. Naruto's continuous efforts to protect Sakura gradually make her fall for him. In contrast, in the original series, Sakura was mainly focused on Sasuke. Fanfiction gives an opportunity to change that narrative.
You can focus on their emotional bond. For example, show how Goku's pride in Gohan's growth and achievements affects their relationship. It could be about Gohan seeking Goku's approval and Goku being there to give it wholeheartedly.
By showing Gine as a protective figure in Baby Goku's life. For example, she could save him from a minor danger, like a small wild animal attack. This would make Baby Goku look up to her more and strengthen their relationship.