I feel like everyone is super OOC but I don't care and I don't have anything to say for myself. Sorry, not sorry.
Harry is transported to the world of One Punch Man when he is forcibly thrown through the Veil of Death after he defeats Voldemort. Everyone who survived the Battle of Hogwarts turned on him and they sentenced him to death by the Veil, not knowing it's actually a portal when used by the Master of Death – though they didn't know he's the MoD either. So he is transported through the Veil and appears in a shimmering flash of light in mid-air right in front of Saitama and Genos while they are heading home after grocery shopping (this is after the show so the Universe was saved by Saitama and nobody knows).
Saitama catches Harry when he starts to fall and since he's unconscious they take him home and try to make him comfortable. When Harry wakes up, it's to loud crashes and rumbles outside as a villain had started attacking civilians and Saitama and Genos went to go help. Harry goes to the balcony and watches in awe as they fight, Genos taking down foes left and right and Saitama finishing them off with one final blow. When they head towards the apartment Harry ducks and tries to slowly crawl back inside but Genos had seen him and they jump up to the balcony.
"…'llo?" Harry mumbles, his accent and bashfulness making his voice garble a bit.
"Hi there, my name is Saitama and this is Genos. We found you earlier when you came out of thin air. Are you doing okay? You were passed out…" Saitama trails off as Harry nods with a wary and uncertain look on his face.
"Who are you and how did you appear like that?" Genos demands, striding forward. Harry scrambles back until he hits the end of the balcony as Genos towers over him. It's then that Saitama and Genos get a good look at the young man. Unknown to any of them, Harry had gone through some transformations from the world jumping. He was in his MoD body, age 17 forever, but his eyes were a bright spring green, closer to the Avada Kedavra spell than ever. His hair was still flippy, curly, and messy, framing his heart shaped face and gently brushing his narrow shoulders. His skin was very pale since he had been literally in hiding for the last 6 months but all of his wounds were healed over, everything visible/that left a mark looking a couple of years old now. He was only 5'5'', barley reaching Saitama's shoulders, so he only came up to Geno's chest. His clothes were a simple pair of plain jeans and a long sleeve, open neck green shirt. His delicate looking feet were bare. Taken aback by how pretty this young man was, Saitama and Genos shared a look before Saitama grinned and winked at Genos who turned back to Harry with a bit of a blush on his cheeks.
"Well?" he demanded again, though this time he stood his ground so Harry wouldn't feel as threatened.
"Um…I'm Harry and….I…was banished? So that's how I just…appeared…" Harry trialed off, realizing that telling two VERY powerful strangers that were already suspicious of his motives that he was banished wasn't very smart so he tried to rush on, "BUT but it was unjustified, they all turned on me! I killed the guy who had been tormenting people for years and they turn around and sentence me to death and then I don't remember what happened before I woke up here…" halfway through his voice started to crack and it looked like he might cry to Saitama's alarm but he held strong and pushed through, finishing with another trail off as he nervously fiddled with the end of his shirt.
Saitama and Genos are sympathetic and offer for him to stay with them until he could set himself up. He does just that and in no time is working part time at the nearby convenient store (the one they frequent). He stays with them for a few months and as they get to know each other Harry hops on the One Punch Man bandwagon with Genos, so they become fast fanboy buddies to Saitama's embarrassment.
All of that was basically because I thought of that last sentence. Harry joining Genos in his fanboy ways makes me happy.