Izuku's quirk is Smoke Warp. It's an emitter type quirk that allows him to form portals from smoke. [Not Kuroguri Smoke, actual smoke from fire or Explosions. The smoke becomes a light shade of green when it's under his control] Unfortunately he cannot produce smoke, only make preexisting smoke into portals.
Inko's mother had that fluid Warp quirk that All for One has. [Apparently its simply called Warping] She went missing shortly after Inko's birth.
[Inko was born in Garaki's Hospital, and Garaki witnessed her mother warp her husband to her by accident during the actual birth]
Inko's Attraction of Small Objects and Hisashi's Fire Breath combined into Smoke Control, however the latent gene for Warping in Inko's Quirk Factor caused a mutation to occur, and BOOM! Izuku got quirk that could control smoke [to a degree, its really just a sub-ability and not the Quirk's main function, so its quite weak however its there] and make portals FROM said smoke.
In order to work, Izuku either needs to be able to see his destination or know their coordinates. Izuku's quirk functions exactly like Kuroguri's, because it is the quirk that combines with Cloud to make Warp Gate. However instead of a purple mist it's green smoke.
[While acting as Dr. Tsubasa, Garaki stole one of the two vials of blood he took from Izuku to "make sure he was healthy" and made a copy of Izuku's quirk for All for One. Since Garaki doesn't have All for One (The Quirk) and knew that people would be keeping an eye on Izuku because of his quirk's nature (therefore he couldn't just kidnap him without drawing attention, he learned that lesson after the fiasco with Inko's mother's kidnapping. It took MONTHS for THAT to die down), it would have to make do. Sadly, copies are 1/4th weaker than the original, so Izuku can overpower Kuroguri if he has enough smoke.]
Edit: I just had an idea! You remember how All Might releases smoke when He's detransforming? What if the smoke was infused with One for All's energy? You could do something cool with that!
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MHA Story And Quirk Ideas
FantasiStory/Plot and Quirk Ideas I have no motivation to make, but think sound really cool! The entries with Quirk : [Name Here] means this entry is about a quirk idea! The entries with Story: [Name Here] means it's a story idea! If they're combined, it m...