HP Idea
Harry (male most likely, though could be female) is in an 'accident', and loses his/her right eye (that's the one under the scar right?). Harry is given a black eyepatch to cover the empty socket and the scar that passes over the socket.
I imagine if it was done by the Dursleys (most likely Vernon), that it was done with a knife in a fit of drunken rage.
And it probably most likely happened before canon (the letter), or it happened when the letters started to drive Vernon 'mad'. Perhaps when Harry has come back from shopping with Hagrid (which in the book timeline is a month [July 31] before term even begins), and Vernon has decided that he must use extreme means to get rid of the magic, even if it kills the 'freak'.
But obviously he doesn't succeed, and is thrown aside (Harry's magic?) before he can cause Harry any further harm. Petunia rushes into the room then, sees all the blood on Harry's face, and an unconscious Vernon against the wall. And for once does something 'sensible' and takes Harry to the hospital. Where the doctor has to remove the whole eye, and stitch the slash wound close. (The knife mark, blends into the curse car, making it one big cut down Harry's face [though it ends before the cheek, so that it is still covered by the patch and Harry's hair]). Harry remains unconscious (from blood lose) for a couple days, and then remains in the hospital for another week or two for observation, and then he/she is released with the patch now replacing the bandages.
Harry goes back to the Dursleys, or what is now just the Evans home. While Harry was in hospital, Petunia filed for divorce, and claimed rights to Dudley (or at least shared custody after the divorce is completed) and moves back to the house she grew up in (which is in Cokeworth? Snape still lives in town i think). She makes arrives when Harry is released and takes him/her with her to the Evans home.
Harry has his/her own room and no longer has to worry about being heaped with all the chores for the house. This responsibility is now shared between the three of them, though Harry's tasks are limited to like washing the clothes and cooking/gardening maybe, since Harry actually kind of enjoys those tasks.
*Dudley starts to turn around once he isn't exposed to Vernon constantly. But maybe he ends up with dual personalities, one when he is with his mom and Harry and the other (more violent) one when he is with Vernon and Marge [Vernon moves in with his sister after the divorce], but it takes a few years for this to actually happen, but either way the nicer side is more common since he spends more time with his mother than his father.
I think eventually Harry is encouraged to get a replacement eye, might take till third or fourth year, when he actually learns more about them and the possibilities.
But once he gets one with all the extras, he keeps it covered with the patch still. (Habit and all that, and people will underestimate him).
He also gets his/her eyesight fixed, so no more awkward glasses. Or maybe he/she started out with perfect vision?
The Evans lived in Cokeworth, and were in walking distance of Spinner's End where the Snapes lived. (The Midlands, England)
Harry either male or female, has red tinted black hair in this universe (kind of like how in anime some characters with black hair sometimes look like they have blue or green hair instead).
Maybe the injury actually happens a year before canon, so all i want to happen, happens.
Harry's clothes become rather punk/goth afterwards and up to maybe 5th or 6th year (where then becomes well dressed, like button downs, ties and dress slacks and shoes.)
He does though get an ear piercing (a little gold/silver dangle? Like Zoro's from One Piece), but not till he/she is like 13/14.
After Harry is out of the hospital, Petunia takes Harry clothes shopping (Harry chooses monotone colors with a few greens and reds thrown in. Most is casual punkish clothing, though there are one or two formal outfits. Steel toe boots/combat boots become the main pair of shoes (though there is a pair of sneakers and dress shoes).)
Harry redecorates the room (which used to be Lily's, Dudley got Petunia's old room), and decides eventually to paint it a really dark blue almost black color and puts glow in the dark stars on the sealing and some of the walls. The bed is a full size, with black blankets. There is a nicer desk and chair, a floor to ceiling bookshelf (only one or two shelves have anything on them), a dresser and a nightstand (with clock and lamp).
Petunia tells Harry the truth and explains what she knows about Magic, she takes Harry and possibly Dudley to Diagon Alley, mainly to Gringotts. The goblins explain the rest of events as they know it, and Harry learns of his inheritance (takes up the heir ring, and picks someone to represent him in the Wizengamot (sp?) and in the press, once he learns of his fame and wealth).
He picks up a pocket watch, one that on one side us like the Weasley's clock (though it only has Harry, Dudley and Petunia for now), and on the other it tells time (which inlcudes time of day, the day of the week, the day of the month, and the phases of the moon and planets?). I imagine that this watch could have belonged to James (he would definitely like the moon phase part to help Remus, and for prank potions). And it already had some hands on it, like Harry, Lily, James, Sirius, Remus and Peter (maybe also the three Longbottoms). When the people on the watch explained (there is a place for dead, or the hands just fall off when that happens), and the goblins realize that it has Peter alive, they start a search for him, and they look into Sirius' situation. They can't do much (though they do make a case, and petition for a trial) until Peter is found.
So Sirius doesn't show up till third year still. Though once he has escaped the goblins put the plan into action, and he is cleared over the summer (though Peter still escapes).
Maybe Harry tries to write letters to Sirius in prison, and gets to know him somewhat through this way. Harry would also write to Remus for the same reason, but Harry would actually get to meet Remus.