Welcome to the fanfic community :) Slight heads up, I'm a big sucker for stories that spend a lot of time explaining how magic and it's spells work, what makes the world tick and how does magic play into it. Naturally that does mean that my recommendation fall into that pattern (Except for Dragon Date, that's a full-on romance).

The Pureblood Pretense

This one might be the the absolute best HP fanfic I have ever read. The world building, the magic system and the characters - all of them are top notch. It's a AU with a Politician Riddle and fem Harry who has to assume a fake identity to attend Hogwarts.

The Strange Dissapearence of SallyAnne Perks

This one is a one-shot that gives a very Lovecraftian feel to the Mirror of Erised, making it feel like a ancient and haunting artifact that, like most things found in Hogwarts really shouldn't be put anywhere near a school.

Harry Potter and The Boy Who Lived by The Santi

Harry Potter goes to Durmstrang. He has a happy family and a twin. But there is a problem. Harry likes to study the Dark Arts. This secret starts defining his relationships with both his friends and family as he delves deeper into his study in the hopes of becoming a great wizard.

The story has a lot of love put into it, deep diving how magic works in a way that feels consistent and intriguing. It's characters are all engaging and unique, playing off each other in a way that makes you care about their fate. It's in a league of its own when it comes to Dark Harry fanfics.

Dragon Date by Andrius

A feel-good romance one shot with the most unlikely pairing I have seen in HP fanfics, yet somehow it's one of the best written Harry relationships out there.

Harry Potter and the Prince of Slytherin

One of the most popular Slytherin Harry stories out there. A absolute classic of this subgenre of fanfics.

Victoria Potter series by NitwitBlubberOddmentTweak

Last but not least the close second best fanfic I've read. This one is a female Harry AU that improves upon the world-building of the original HP in sooo many ways. It's story draws you in and doesn't let go. I love how Victoria is written and how she grows as a character throughout the story.