I do not own Harry Potter, or Batman. This isn't even my idea. I haven't see someone do a story from this but I did read a Harry/Joker oneshot, with Hermione as Harley Quinn

Vernon Dursley was, for once, a happy man. He had just been offered the chance of a lifetime. A large chemical company, "Axis Chemicals" was after a large number of drills. They had discovered a way to make a rare and valuable compound, cheaply and on a large scale.
A porous rock was left in a vat of chemicals for a few days, removed, drilled open, and then the extracted innards were chucked in a boiling acidic mixture for one week. The original drill supplier used inadequate drills that kept breaking, so Axis was replacing them.
A few drill companies were to tour the factory with their families, before meeting the manager one-on-one to discus drills. Landing the deal would get Vernon a promotion for sure.
Vernon had a plan, to land the deal, rid himself of his freeloading freak nephew, and get a nice compensation check from Axis...
A man by the name of T.M. Riddle had a similar plan, be rid of those pesky Potters, kill the chosen one, live forever ruling the world. That worked oh so well for him, one fateful Halloween.

At the age of eight, Harry Potter should have known that the Dursley's did not do anything nice for him, out of the goodness of their hearts. He did, however, know that the smirk on Dudley's face promised that he, Harry, would soon suffer.

Most parents would not ask their son to commit murder, but then, MOST parents wouldn't want an eight year old dead. Besides, Dudley was to young to be criminally responsible, and Vernon and Petunia would be too far away to stop him, so how could it be their fault.

Harry knew something was wrong. Dudley's "I'm gonna hurt the freak" smirk kept appearing on Uncle Vernon and Aunt Petunia. Dudley had behaved all the way through the long car journey, and all through the tour. Seven hours without once getting Harry in trouble. Harry had passed terrified so long ago, he was approaching calm from the other side.

The tour was nearly over. All that was left was to take the high walkways over the factory floor to the managers office, where each Drill representative would enter the office in alphabetical order and do a five minute sales pitch on prices and why Axis should choose them. Vernon was first. He entered the office according to the plan, and that's when it went wrong.
Dudley always had a short attention span. It was why Harry suffered so much. Whenever Dudley got bored, he got Harry in trouble. Dudley stopped listening at the most important part of "The Plan" when Vernon explained it to him. Therefor, instead of waiting, like he was told to, until Vernon was on the way OUT of the office, pitch done, Dudley struck on the way IN.

BASH
"AAARGH"
SPLASH

Dudley shoved Harry off the walkway, into the boiling acidic goop.
The acid was not strong, but it was hot, and not a good place to go for a swim.

By some miracle, doctors were able to stabilize Harry within just three days. In an odd coincidence, the day of the accident coincided with the Magical Ministerial Elections, as one leader leaves, and an incompetent halfwit who follows the money takes over, Chief Wizard of the Wizenmont, Albus Dumbledore is busy counting votes and filling forms at the ministry He is so busy with paperwork he sleeps in his office at the ministry in a conjured bed. The alarms at Hogwarts go unnoticed, and since the portraits were ordered never to mention the Harry Potter alarms to anyone under any circumstances, they are unable to tell the headmaster, on his own orders.

For six weeks the doctors kept Harry unconscious until he had mostly recovered from surgery and they could remove the bandages. It was time to find out what the "Accident" had done to his mind...

Harry woke up in a strange place. It was large, far bigger than his cupboard, brighter too. He could feel bandages on his face, and see a pretty nurse by his bedside. She quickly ran to the door, stuck her head outside, and shouted "Doctor! He's awake!".

Several doctors hurried into the room.

"Hello mister Potter," an elderly, bald man said, "We weren't expecting you to wake for another hour at least." He quickly moved to Harry's bedside. "I'm doctor John Smith, you've been in an accident. How are you feeling? Do you remember what happened?"

"I feel great." Harry said, "I just have this happy feeling. But I don't remember what happened, sorry."
Just then, a pair of large fat flies landed on the doctors head. Harry began to giggle. When the two flies began, uh, making another fly, Harry roared with laughter.

"Whats funny Harry, you don't mind if I call you Harry do you?"

"It's fine," He replied, "it's just there some flies on your head being naughty."

The doctor quickly shuck them off, to the amusement of his colleagues. When Harry calmed down, the doctor told him he had been badly hurt, and it was time to remove the bandages to check the scaring.
They unpeeled the bandages, and handed Harry a mirror.
"I, I look like, like a, a clown." Harry began to giggle again. "I'm a freak!"

Harry's skin had gone white, his scar had paled, his hair turned green. Because his skin had sort of melted, when the doctors put it back together it distorted, giving Harry a fixed, forced grin.

After a few more weeks in hospital it was time to go home. Harry had been declared "Unstable but harmless by the hospital Psychiatrist and aloud to leave. When Harry got home he was shocked to find he now had a bedroom. It turned out Axis gave uncle Vernon a large payment not to sue, and the government gave them a nice check each week to look after their unstable nephew. He was no longer a "freeloading waste of space". His food, clothes and board were paid for, and they could afford to get Dudley even more expensive toys then before, so he was OK with losing his second bedroom, as his new stuff made the old stuff rubbish. There was even some money to hire a gardener to come round once a week, so Harry had less chores to do. There was just one problem for the Dursleys. In his madness Harry's brain was constantly stimulated enough for accidental magic, and he was in control of it...

By the time his Hogwarts letter came, the Dursleys were starting to hate Harry again. He was unbalanced, and they had doctors notes to prove it, so they did not have to worry about their reputations. The neighbors my have resented them a little, because Harry was annoying, but there was a lot of respect for anyone kind enough to look after someone like HIM.

From turning a toupee into a clown wig, to making the headmistress honk like a goose whenever she got mad, all the way up to vanishing the back of the police chiefs uniform, mid parade, Harry was certainly a Joker.

The main problem for the Dursleys was that Harry knew what he could do. After the waste returning toilet, that made Vernon walk funny for a month, they realized he would win. Fortunately, Harry valued his word above a few laughs, and they were able to make a deal. Petunia explained Harry's heritage, and the Dursleys agreed not to punish Harry for any prank, and Harry promised not to prank the Dursleys, and to stick to jokes that could be done non-magically. That is not to say he stopped using it, but levitating a pie into someone's face was a little hard to explain.

One thing that did improve matters between them, was that as Harry could use all his magic, with perfect control, he was able to do things for them that many not even have a spell invented yet. Uncle Vernon had not needed to put petrol in his car since the week after the deal, and Dudley's toys were repaired in moments. Clothes would not stain, both Vernon and Dudley were slimming. At eleven Dudley was as light as he had been at six, which is to say he was chubby, rather than egg shaped. With weight loss came increased energy for Vernon, which improved his temper as he was no longer permanently tired. This led to a better attitude at work, and got him a promotion. This helped them overlook the fact that Harry now had a bedroom bigger than the rest of the house. They could not stop it happening, and were not going to let the freakishness go to waste, but it made them feel... ...dirty... ...tainted. They went to church every Sunday now, and Petunia started rubbing her crucifix whenever she was in the same room as Harry.

As Harry could already do pretty much whatever he wished with magic, the Dursleys were happy for him to go to Hogwarts when he got his letter, as he would be the other freaks problem for most of the year, returning just in time to help Vernon and Dudley regain their figures over the summer. A reply was sent with the owl that delivered the letter, asking for "someone who can act normal" to take Harry for his school supplies. With a comment that the Dursleys did not consider Harry their responsibility, but their problem, and that they refused to spend so much as a penny on his unnatural education.

The person who came to collect Harry to buy his things, would be in for a shock.

JokerPotterJokerPotterJokerPotter

Unfortunately, Harry had been overlooked when they had planned the staff holidays around the needed trips to diagon, and only Hagrid had the spare time to escort Harry, and show him around. Hagrid, however could not act "normal" due to his size. Minerva had an idea though.

Dear Mr Potter.

Under British law, no witch or wizard may own a wand until their eleventh birthday. As such, "someone who can act normal" will be arriving at your house at 9 AM on your birthday. If this is an inconvenience, the visit can be delayed two weeks, but may not allow sufficient time to look through all of your new books.

Please send confirmation either appointment with this owl.

Professor M McGonagall

Deputy Headmistress

Hogwarts

Hastefully written on the other side was a note saying "Birthday fine, the sooner the better."

When he saw it, it took three hours to get Snape to stop muttering things like "arrogant as his father" and "spoiled little brat". Harry's reply was a little rude, but acceptable from an exited child.

His birthday arrived, and Harry even got presents off the Dursleys. After all, with one of "them" visiting today, they couldn't afford to look like they mistreated him. Harry was actually quite popular at school, despite pranking his friends on a regular basis. Mostly because Dudley was slightly scared of his cousin with his freakish powers, and would not attack Harry's friends. Other bullies became the targets of the nastier pranks Harry came up with.

At 9.00 AM, precisely, the doorbell rang.

The stranger had appeared on privet drive fifteen minutes before. The stranger was nervous. First impressions are important, especially so in this case, considering...

The stranger shook their head. Thinking about what could go wrong would just make them more nervous, and more likely to make a mistake. The stranger looked down at their new suit, bought especially for the occasion. They did not often waste money like this, but this was important. This was Harry freaking Potter, and the stranger was to be the first magical he met. "Don't screw up. I must not screw up. I will not screw up."

The stranger took a deep breath, and reached for the doorbell.

That evening...

Minerva hurried through the corridors cursing, not for the first time, her age and the castle's sheer size. Finally she reached the hospital wing, and ran to Lupin's bedside. "Are you alright, Remus? What happened?"

"Do you remember, Professor, I once told you I wanted to be a teacher, but knew it would never happen?"

"Yes" She replied, hesitantly.

"I am really, really glad I am not now. I hope never to be in a position of responsibility around Harry again."

"Why Remus, what on earth..."

"Imagine Merlin, with a marauder attitude. Then add some extra chaos."

As one, the staff of Hogwarts felt a shiver down their spines. Filch shuddered violently, and a tall dark haired man in the dungeons began to feel very cold. Elsewhere a dark lord began desperately to come up with a way to resurrect himself without being in the vicinity of a certain eleven year old. Unfortunately, all the methods he knew required remaining in the country, and none could be done properly without access to Hogwarts. For the first time since that Halloween, Tom Riddle regretted his career choice.

"What happened?"

"Well prof... Minerva, it started in Harry's room..."