AE's Timeline is customizable in terms of what you see. That area you circled is known as the Switches column. It is there by default. You or someone else must have inadvertently set it to not be displayed.
To get display the Timeline's Switches panel, right click on any column header in the Timeline and go through the menu that appears after you right click. Select Switches. If that doesn't work then click on the left-most (from a set of three icons) icon at the bottom-left of your Timeline.
The keyboard shortcut to toggle the switches/modes columns is F4, and the shortcut to toggle the parent column is Shift+F4.
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