I do not think RadToolTip is the right tool for this task. For one thing, there may be several such notifications/numbers at any given time, while only one RadToolTip can be shown.
Also, with its default borders and padding it would be rather difficult to make it so small.
What I can suggest is placing another HTML element inside the buttons/images wrapper (in the screenshot example - the globe or messages wrapper). That main wrapper can have position: relative; and the custom element that will show the notifications count can have top: 0; left: 0; position: absolute; in order to be shown at the top right corner. It can have a desginated CssClass so you can access it on the client if needed and create its styling, and it can be runat="server" so you can access, show and populate it from the server if needed.
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