I had this happen to me, on an iPhone 6SE, as a result of downloaded about 200 emails, while my email server was off line for a while. Clearly, these are bogus emails and it indicated a corruption the index to the email database. However, the fix is a simple as turning off the phone and turning it back on (at least in my case).
The concern I have with the fix, above, is that it goes too far. You probably won't have to RESET all of your phone settings. Also, the solution suggests that you can find out which email account has the phantom emails, but I was not able to find them in any of the individual account inboxes, only when I looked at all the emails.
iPhone 6SE 16GB (two weeks old)
IOS 9.3.3 (most current, as of today Aug 14, 2016)
4 POP accounts (10,000 emails, all in Folders, less than 40 in the inbox)
1 Gmail
1 iCloud