the rules say that you can't modify the game after you submit it, I would like to update it, but not for the jam... if I update it will the old version remain in the jam? I don't want to do something wrong

You can not update until the voting period ends. Itch.io will not allow when we mark the lock game files. It will lock the uploads. 

As long as the game is in the jam and voting period is running you can not update the game files. After voting ends you can edit and update like normal.