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 such fanfictions, Goku might develop by becoming more of a mentor to Gohan. He could teach Gohan new fighting moves and also how to control his emotions better during battles.
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.
One possible interaction is that Bardock could spar with Goku and Gohan. He'd test their limits and see how much they've learned about fighting. Another could be Bardock sharing stories of Planet Vegeta with them, which would be really interesting for Goku and Gohan to hear.
In the manga, Gohan never managed to defeat Goku. Their battles often ended with Goku coming out on top or the fight being interrupted for some reason.