Check the metadata settings in your preferences. There's an option to write metadata to your clips on disk and it's probably checked. What happens is that you add a maker to a clip and Premiere actually updates the original file to indicate a marker was placed; that marker would appear in every project the clip was loaded into. Because your duplicate clip is just a copy within Premiere -- and not a separate file on your disk -- the marker appears on both.
Turn off that setting in the prefs and this will resolve it.
There are no "metadata"settings in preferences. Maybe you meant the media section in prefereces: there, I unchecked "write clip markers in XMP" , but it doesn't solve the issue and i still have markers on both copies and original clips.
PS: I also unchecked "Enable clip and XMP metadalinking" ... None of that solved my issue.
In my case, working on stuff, when I know I'm gonna change stuff I use 'save' and 'save as' a LOT.
So, in your case you know you're gonna make a copy. Save the project, and 'save as' ... for example,
film-1, film2-copy with markers.
You use whatever names describe your progress through the project.
It's kinda like a workflow that just works OK depending on what edit program you are using and your computer resources, etc. But organization and separating stuff as project milestones is important no matter what you use as editor.