Why does the email app on my Samsung Galaxy S4 keep loading old messages and telling me they're new?

So I've recently upgraded to the Samsung Galaxy S4 from the iPhone 4. I seem to have correctly added my yahoo mail account. However, every time the phone checks for mail, it will indicate that I have 17 new messages, when in reality there may only be three new messages. What is happening is that as I delete messages, the phone seems to be pulling older messages from my yahoo account and loading them as new, even though they have already been read on my PC. At first I just re-read them on my phone to clear the icon number indicator, but the the minute the phone does another push from my account, it happens all over again. The Verizon tech person there's nothing I can do about this, but I can't believe that's true. Any help on how to solve this would be greatly appreciated. Thanks, Marcella