What does this blue dot in the Dock in Mojave mean?
I've seen instances in the past when certain app icons appear incredibly small in the Dock, to the point that clicking on them does nothing. The icon in your screenshot looks very similar to the Twitter icon, so if you're a Twitter user it could be that.

Regardless, I would start with restarting the Dock as a first step. To do this:


Now open Terminal (usually located in Applications > Utilities)
Enter this command killall Dock
Press enter


Once you've done that, use your Mac for long enough to know if this has resolved the issue. If it hasn't, then you can do a reset and restart of your Dock as follows.1

To reset and restart the Dock, follow these steps:


Go to Finder
Press and hold the option key down
Now go to the Go menu
Select the Library option to open the User's Library folder. You can let go of the option key now.
Go to the Preferences folder (i.e. within the Library folder)
Find and move the com.apple.dock.plist file to the Trash
Now open Terminal (usually located in Applications > Utilities)
Enter this command killall Dock
Press enter


Once you've done that, use your Mac for long enough to know if this has resolved the issue. 

1. IMPORTANT: After doing this you will need to re-add any non-default icons (i.e. apps) that you've added to the Dock. Before proceeding you may want to take some notes (or a screenshot of your Dock) as a reminder of what you had there previously.