I might be mixing multiple fics with this one, but I think they were the same or I read them around the same time.

So it starts off at the end of third year. Sirius decides he needs to recover from Azkaban and wants to spend time with Harry. So he takes Harry to America where they go to a healing facility that is part of a time bubble. No matter how much time you spend there you leave the area exactly I think it was a week in the future.

Harry learns some native American magic which helps later because in year 4 he uses a native American war spell to take down the dragon and he either does a ritual or creates a runic staff that splits the black lake like Moses to rescue his hostage.

I originally was thinking it was Harry Potter and the lightning scar, but while there were similarities none of the details I remembered matched up.