In Yahoo! Messenger, click the Messenger menu and choose Preferences. Go to the Alerts and Sounds tab, and do the following:
-Select from 'Alert me when' the option 'I receive a message in Yahoo! Mail'.
-If you want to disable the icon notification of new e-mail messages from your taskbar disable the button 'Showing an icon in the system tray'.
-If you want to disable the message notification of new e-mails from the right bottom corner of your screen, disable the button 'Showing a message at the right bottom corner of my screen'.
-Click Apply and close Preferences window.