Apps icon in the dock bar randomly rearrange by itself

Items can be on the Dock in one of three ways.

1. you have dragged them onto it
2. the applications are currently running
3. new to Catalina - they are recently used but not running. These will always appear on the right side of the Dock if it is on the bottom of the display or on the bottom of the Dock if it is on the right or left

Icons that are dragged onto the Dock should always appear in the same location whether they are running or not. Icons of applications that haven't been dragged onto the Dock will appear essentially in the order in which they were launched. This, I would expect, is why your icons change position. And if you are running Catalina the #3 would add to that confusion.

If I'm correct, your solution is to drag the icons of programs you run frequently onto the Dock so they remain in the location you want them.

Use the Dock on Mac - Apple Support

Change Dock preferences on Mac - Apple Support

I will add to this schematic— the far left side would Continuity & Hand Off apps.

Use Continuity to connect your Mac, iPhone, iPad, iPod touch .

Handoff - Apple Support

Could be corrupt plist  —delete the com.apple.dock.plist

Finder>Go>Go to Folder    copy and paste:

 ~/Library/Preferences/com.apple.dock.plist

reboot or in terminal copy and paste:

 killall Dock

Your computer is haunted 😱

Are you running any utilities that interact and/or change the behavior of the Dock - like HyperDock? HyperDock, BTW isn't causing me problems. But another such program might be involved.

Also, have you tried creating a new account and seeing if the Dock is misbehaving there? This would tell us whether the issue is global or limited to your account - which would help a lot.