Most likely you are using email tags, say all emails containing a specific word or from a sender or domain get tagged? It would then give you a notification that you have new email, and another notification that you got a tagged email, all for a single received message. You will know if this is the case if you click on the tag notification it links to all messages with that tag, rather than your inbox. This is easy to miss. After clicking the notification, you will either be at the email or in a "folder". If you are in the folder, look at the other messages. Do they all share the same tag you set up? If you are at the email, just hit the back button to go to the folder.
Go into your Gmail account settings and disable the notifications for each tag category.
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