Does anyone know this icon? I can't get rid of it.
I don't recognize that, but you can usually figure out any menu bar item by clicking it or option clicking it. You can usually option drag any Apple item out of the menu bar to remove it:
If not in this specific case, go download this menu bar tool and start digging into what it tells you about that item.
Alternatively, you could isolate this to a user process or system process following this guide:
Once you know if it's a system or user program, you can look at all the places where apps start and figure what software was installed to make that icon. You could save all work and make a system backup and then start killing user processes in Activity Monitor one by one that belong to your user to see which process makes that icon. It's likely not anything from Apple, so simply uninstalling all third party software would be a last resort.
Most programs, but not all, will show up in Login Items. System Preferences > Users & Groups > click the Login Items tab.
Alternatively, close all open application, then open the Applications folder > Utilities Folder > launch Activity Monitor.app, and then click the "User" tab twice.
Look for the asterisk icon you posted in the screenshot:
Under Process Name. That should give you an idea what program it belongs to. If the application name isn't displayed there, click the Process Name to highlight it, then click the (i) button for more info.