Many apps can send notifications, and any number of them can be set to send them at a specific time of day.
After the notifiction, be sure to pull down the Notification Center from the top and see what's there. It may show you any recent notifications. You do this by sliding your finger down from the top edge of the screen. Make sure you have Notifications selected, and not the Today screen.
For Apples own apps besure to check out Reminders and Calendar for re-occring events or items.
Another app I have that might do this is Dark Skys. It can send you a daily summary of the weather. 9am is the default time. This isn't he only thrid party app that can give timed notificications. Search through the mostl likely culrites. Apps that might have a reason to notify you of something daily.
If all that does not help, then you'll have to go through all your apps in Settings > Notifications and see what is enabled. You won't find any timed settings here (those are only set in the app) but you can disable all notifications from an app. You'll also see wether they will show up in the Notification Center. You can use these settings to troubleshoot the problem; turning on/off notificatons or the Notification Center to see what happens the next day.
Good luck.