Thanks for the extra info.... now I believe I know what you are referring to..... the new version of Yahoo Mail allows users to chat with folks that are in our address book and to receive offline messages from those chat friends.... This is my setting about chat

In addition to listing yourself as busy or offline (click that down arrow and choose the status you want to be displayed to any friends that all use yahoo and are in your address book).... You can also click on the Options setting on the top right of the Yahoo Mail page... Then on the settings page that opens, the first tab is for General settings and the very first choice is whether you want to get messages or have messages.... I don't have a check mark in my settings, as I don't do chat or message sending with the Yahoo Instant Messenger service, so where my page as I picture above shows me offline there is no indication about any offline messages (Yahoo IM).... If you don't do messaging with IM, then you can also do your General Options mail settings to not even have a check mark in that messaging section.... Then you won't get that offline message notice anymore.....
Hope I explained that where it makes some sense.... getting late, and I should get some shut eye so I can be understandable....

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I'm pretty sure we are speaking of the same thing, in this case offline messages are just IM's or messages sent by chat buddies.... and of course, likely an advertising message of some sort from Yahoo..... I've never received a spam message since I don't receive offline messages, any spam messages are just in my SPAM folder and are deleted without me even looking at them...
If you were to click to go back to the old Yahoo Classic mail format, I don't think you could get any notices of offline messages as I recall, you just miss the appearance of Outlook Express mail which Yahoo is trying to give us.... I've got 6 different Yahoo mail accounts for different purposes, but use the new version of Yahoo Mail for all of them (Ymail.com, Rocketmail.com and yahoo.com domain accounts from Yahoo).
Good luck, and let us know if this offline message area and settings will resolve your question... Al