His quirk could be something like super - speed regeneration. In the original Naruto series, he has a great deal of stamina and the ability to heal relatively fast. But with this quirk, he could recover from even the most severe injuries in seconds. This would mean he could keep fighting no matter how badly he was hurt, and his enemies would find it extremely difficult to defeat him.
In the manga, Bakugo has had many significant moments. He's dealt with internal struggles, formed new friendships, and taken on challenging missions that have shaped his character.
Often, they portray him as frustrated. Without his quirk, he loses a big part of what makes him feel superior, so he's likely to be angry at the situation and those who look down on him.
In some fanfictions, Bakugo can become more empathetic. For example, if he experiences a situation where he realizes the pain he's caused Deku over the years. His aggressive nature might soften as he starts to understand Deku better. Deku, on the other hand, could become more assertive. Instead of always being the timid one, he might stand up to Bakugo more firmly in fanfiction scenarios.
Maybe they could combine Naruto's Rasengan with Bakugo's explosive power. Picture Naruto forming a Rasengan in his hand and Bakugo adding his explosive energy to it, creating an even more destructive and concentrated attack. This would be a really cool combination in a fanfic.