Hello!

I'm looking for a manga in which a main character has some sort of special power which translates to regular people being scared of him/her. Yet he/she meets up with the opposite gender and that person is not afraid, accepts the difference, and supports him/her.

-Romance please!
-Preferably girl who has special power
-More action/detective instead of school-life
-Character with special power has faced some sort of societal rejection before
-No yaoi/shounan-ai or yuri/shoujo-ai please (I don't mind if there's a side plot of it though)

Some examples would be...
Arcana (KOTEGAWA Yua)
Keishichou Tokuhanka 007 (What brought about this topic)
Mekakushi no Kuni (Except this is school-life)
Absolute Witch
Siesta (Although the story hasn't developed as far)
Beast Master (Male with "special power")

If you can call a scary face a special power then try Angel Densetsu lol.

I don't know if it's exactly what you're looking for, but The Demon Ororon is a good one 😉

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Variante

Not alot of romance but pretty much what your looking for...

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“As he read, I fell in love the way you fall asleep: slowly, and then all at once.”
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From Far Away - it's the guy who has the scary powers, but the "everyone's scared of me except you" part is a main reason he falls in love with her. The story is very cute and romantic, lots of action, he has trauma from societal and personal rejection, and it's so sweet how accepting the girl is of him.

I would suggest Iris Zero, but that's oddly enough the exact opposite of a few things you specified, but hits the "everyone else is scared of but not them" specification head on. The manga revolves around a character without a power in a world where most people his age have powers. Also the main character is a guy.

Second from far away

exactly what your asking for word for word 😃

except for the girl having the power, but the important part is there 🙂

"Religion is like a gun, It's only as good as the people holding it and it can easily take a life."

                             -Personal thought

You could try Shinrei Tantei Yakumo.
I haven't read that version, but I did read Shinrei Tantei Yakumo - Akai Hitomi wa Shitteiru (the first one I mentioned is an alternate version) and it fit most of what you were looking for.

Fruits Basket
Highly recommend that!! 😁

In Naruto, naruto hast to work to get people to accept him, and there are some other characters like that. if your after romance, i advise Beauty is the Beast,the main guy terrifies everyone except this one girl who changes his name from Wanibuchi (or something like that) to Wanichin.

Only Naruto has special power stuff, and that is a guy, Beauty is the beast is just a normal, if not scary guy and a really wired girl.

We work in the dark, we do what we can, we give what we have, out doubt is our passion and our passion is our task, the rest is the madness of art. Henry james

Mamotte Agemasu

Not trying to hijack this thread or anything, but I'm interested in basically the same thing except instead of just special power it's any kind of special trait/strength, and widening the single person to a group of companions (i.e. Berserk and Boku wa Tomodachi ga Sukunai). Romance is optional.

Hanatsukihime fits a bit:
http://www.mangaupdates.com/series.html?id=24808

Dusk Maiden of Amnesia kinda fit in a way.... Not so much i guess...
Yandere Kanojo though i don't think you're looking for this type

orange marmalade might be going in that direction. Vampires exist but they're a shunned minority(people think they're monsters). The main character is a vampire girl that pretends to be human and despite her best efforts gets involved with humans.

Claymore Not out and out romance. The heroine is a member of a group of warriors that hunt and kill human-eating shape shifting monsters. Though to fight them the warriors have to become part monster themselves causing normal people to fear them. She befriends a boy.

Feed your head.