Percy Jackson meets Harry Potter

Kronos accidentally changed something in the past using his power over time. But he didn't directly change anything to do with Percy Jackson, rather he changed something in the Harry Potter timeline. But because it happened in the past, he himself didn't realise the change.
Percy Jackson was betrayed after the war by the gods, and was sentenced to eternal punishment in Tartarus, until an unlikely threat becomes known and his assistance is once required.
Meanwhile Harry, after the wizards war, starts having dreams about Percy. He tries to find Percy, even going to America to do so, but is unable to find him. He doesn't know Percy is from the future.
The fates, however, don't approve of this change and how it will impact the world, so they use their power over fate to keep things as normal as possible, but their power over fate is limited therefore they need to send a hero to ensure everything goes back to normal, otherwise the future will be... well... very different.
Read on to find out what happens when Hogwarts finds itself stuck in the middle of Greek myths.
(A/N: I will try to make this as original as possible, unless a cliche cannot be avoided).
Set after the HOO series (with some editions for the sake of the plot) and after the Battle of Hogwarts.