Tiny red square in my MacBook Air's Dock

First, let’s see if this issue happens in Safe Mode:

1. Shut down your Mac.
2. Press and hold the power button on your Mac. As you continue to hold the power button, your Mac turns on and loads startup options. When you see Options, release the power button.
3. Select your startup disk. It's named Macintosh HD, unless you changed its name.
4. Press and hold the Shift key, then click the “Continue in Safe Mode” button below your startup disk.
5. Log in to your Mac. You might be asked to log in again.

If the strange behaviors do not occur, then it may possibly be a software issue.

If the issue doesn't continue in safe mode:

Leave safe mode by restarting your Mac normally, then try to reproduce the issue.

If the issue doesn't return, it might have been resolved by the other things that safe mode did at startup, such as checking your disk and clearing caches.

If the problem persists, then let’s try this:

• Software Update.
• Use Apple Diagnostics to test your Mac.

Need more help?

• Call 1-800-APLCARE.
• Contact Support.
• Mac Support.
• Mac User Guide.

Good luck! 👋🏼😉

"Tiny red square on dock on macbook?: I just noticed a tiny red square on my dock on my macbook. What is this? It stays there, even if I quit the apps next to it, so it doesn't seem to be connected to an app. Left hand side of the Books app. Any ideas?"

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Thank you for the screenshot.

Dot on the Dock:

A. Safe Mode:

Try booting in Safe Mode. See if it then goes away. Go here: Start Up your Mac in Safe Mode – Apple Support

B. Update your Mac:

Perhaps there was fix for this in the most recent update. So, update your Mac: Go to: Apple menu > About this Mac... > Check for Updates...

Prior to Updating, Back up your Mac:

Create a Time Machine backup of your Mac, so that you can have something to restore your Mac from, should anything go wrong with the update.