For extra information and such that isn't fully discussed through PMs or already in the main thread.... Ideas are just put here for easy reference and further fleshing out- keeps things more organized I think.
Main thread here
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Harry Potter as Headmaster
So I know that in the actual HP series, Harry becomes an auror, so maybe he used to be one before becoming headmaster in the context of this RP. He'd have experience in protecting himself and investigating situations and people; even though teaching isn't exactly his strong suit, he's a good guardian to the school and has the respect of those attending.
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Origins of Magic
We discussed an ancient demon possibly being the source of magic though PMs. In YYH, exposure to a demon's presence or other spiritual energy, can lead to spiritual awareness in other people who wouldn't normally have it. So it wouldn't be a far cry to say, in ancient times, a very powerful demon existed in the western world; this demon's reign of chaos over Europe led to many becoming spiritually aware. Humans grew stronger in the presence of the demon and its minions, eventually learning to hone and control their abilities. One day, when they were organized and able, they teamed up against the demon and sealed it away- bringing peace to the world for the first time in ages.
However, sealing the demon away had adverse affects, for without its constant presence feeding their powers, the humans grew weaker over time- some even lost their powers all together. Thus was the creation of wizards and muggles, and generations allowed for those in between- such as mudbloods and squibs- to be created as well.
Yet the flow of time allowed this tale to be forgotten, and very few are left in the world who have even heard of the legend, much less understand it fully.
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The Object
When the demon was sealed away, he left behind an object, hidden at the site of his 'burial', so that one day he could rise again.
We haven't entirely decided what this is going to look like, but perhaps it could be kinda like a 'prehistoric horcrux'? Not as advanced as the ones that Voldemort was able to create, but something that still had a fraction of the demon's power in it-- which could break the seal on him if fully awakened?
Despite the fact that it holds only a fraction of the demon's power, it's still incredibly powerful-- hence why certain people who know about the legend pursue it, even if they're not sure if it's real.
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The Descendants
We have two OCs, twins, who are descendants of the sealed demon-- much in the same way that Yusuke is descended from the Mazoku. The blood has been lying dormant for years, to the point that they are entirely unaware of their origins or ties to the legend. During the reign of Voldemort, they developed spiritual awareness-- not just wizarding magic-- but the ability to sort of sense the dead and spiritual energy (like how YYH characters do); this was what allowed the demonic blood in their systems to stir. If only a little.
After Voldemort's fall, they grew up peacefully, and did not think much of their abilities. However, these abilities, so small in development as they were, were still enough for the ancient object to begin to awaken; as they grew more powerful over the years, and unknowingly roused their demon blood more, the object grew more unstable as well.