Email App Sync Issue with Gmail Account

[AC Question]

Good day, I am currently using the Pre-Installed Email app that came with my Samsung Galaxy s4. My hotmail account syncs just fine with the Email app, however, my gmail account is another story. I have compared all notification and sync settings between the Hotmail account and the Gmail account, and all notification and sync settings are the same and the correct ones. However, when I open an unread email on the website gmail account, the push notification number of unread emails showing on the email app in my galaxy s4 does not sync, (meaning that it does not drop pero email I open directly on the website gmail account). Whenever I do the same on the website hotmail account, the push notification number automatically syncs with the Email app in my phone, as soon as I start reading emails directly on the website hotmail account, the push notification number for unread emails on the Email app, starts to drop automatically. Additionally, when I enter the Email app on my phone, and hit refresh inside my gmail inbox, or even the combined inbox, it still does not sync with my Gmail account, so Im stuck with unread emails on the Email app, even though I have read them already on the website account. However, once I open each and one them inside the Email app, they become marked as read, and no longer show as unread push notifications, which could represent a more general problem with the Email app or maybe even the phone equipment if it did not happen, however it is not the case.