Disk Not Ejected Properly - Backup of -- not an attached device

Open Disk Utility and see if there's an item with the jMiniPro23 name.

Also, give this a try: boot into Safe Mode according to How to use safe mode on your Mac. Reboot normally and test to see if the problem persists.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

Those setting are in the Energy and Lock Screen sections of System Settings.

As a test

Turn On "Prevent automatic sleeping when display is off"

Set "Turn display off when inactive" to 5 or 10 minutes

Leave the Mac Mini On and only allow the display(s) to turn Off

Do not manually Sleep from the Apple Drop Down menu

Shut Down the Mac when away for a day or more

What USB hubs, docks and other devices are connected to the Mac mini..?

Is there a USB Flash Drive, USB External Drive or a NAS connected to your Wi-Fi router..?

Do you have a Flash Drive, an SD card, a GoPro, a Trail Cam or something like that connected to the Mac mini...?

After you finish your investigation I would not use sleep anyway. It only causes all kinds of issues including drives not ejected properly notifications after waking from sleep. Just have display turn off after a set time.