Android - How to turn off Yahoo Mail notifications in 4.1.2.?

When such a notification appears...

1. Open your notification area
2. Long-press on the notification. This opens the app's settings in the system configuration.
3. Here you can disable all notifications from the app.

This is a feature introduced with JellyBean -- as you've stated your device is running Android 4.1.2, this setting should be available to you.

In the official Yahoo! Mail app, Yahoo recently changed the layout so that the Settings menu is no longer accessed by pressing the "Menu" button.

Launch the app and tap the little < arrow next to the "Inbox" label on the upper-left corner of the screen. This will reveal the Folders menu. Scroll it down to the "Tools" section, tap on Settings, then tap on Account settings option, and finally on Notification Settings. From here you can set up the notification options for new messages:

• Choose Sound -> No sound -> Done to disable audible notifications,
• Use Vibrate to toggle vibration on and off,
• Show in Status Bar to toggle the icon in your Notification panel.

If there is no "Notification Settings" tap the text that lists your e-mail address associated with the account, and you will find the settings there to shut off notifications, both audible and visual.