Azure DevOps, extra packages in Artifact Feed
That because your private Nuget Feed set nuget.org as an Upstream source by default if you set Package from public sources enable when you create the this feed:
When we download any packages from the Upstream sources, it will been cached in the Artifacts, you will see and use it next time without download it again.
You could use the source filter to select the source of the package:
To prevent that, you could select the radio button Only use packages published to this feed when you configure your private feed.
For those feed which you select the option use packages from public sources through this feed, you could delete the Upstream sources from setting->Feed settings->Upstream sources, select that upstream source you want to delete. BTW, for those packages that are already cached, you need to manually delete them.
Hope this helps.