What makes a story and gives it its structure is the character arcs of the main characters. They need to have some kind of flaw that can be exposed, illuminated, explored, and ultimately resolved over the course of the whole story.
A non-omnipotent god needs to either have antagonists that rival or even outweigh him, this essentially makes the character a demi-god, this is also the realm of myth and comic books. So you might read a bunch of those for inspiration.
Nothing is a hard and fast rule, and Superman is generally written without any major flaws, but Superman writers tend to play into the fact that he’s not actually omnipotent to gin up the drama, particularly when villains impose moral dilemmas onto him that he has to solve. This is such a meta-aspect of Superman that die-hard Superman fans complain when you give him flaws to work through. He’s Superman, he’s not supposed to have flaws, not even character flaws, stop being lazy and make the story interesting anyway.
This has the effect of reflecting the usual character arc where characters explore their flaws back onto us. We read ourselves into Superman and so we have to explore our own moral weaknesses in contrast with Superman, who has none.
Another great series to mine ideas from is One Punch Man, which is a brilliant semi-parody featuring a massively overpowered main character. His story of trying to regain the zest in life that he lost when he acquired his massive abilities is interesting enough, but what really allows it to shine is the supporting characters, who, because of the lack of any real challenge to the main character, are allowed to share his spotlight in fascinating and unique ways.
But first you have to decide exactly why you want to make your character a god. A god in what way, what advantages does he / she have over everyone else and why is this interesting from a story standpoint. Everything in a story should be cohesive, it all needs to fit into the same overall structure and narrative. You need to go over it with a fine toothed comb and ask yourself of every plot point and detail element, “what is this adding to the story?” As opposed to adding to the world or scene.