1. "Publish to subscriptions feed and notify subscribers" is only to NOTIFY your subscribers. This setting is in the "Video details" page when you're in the process of publishing your video for the first time. The setting is located under "Show more" ... "License and distribution".

2. If you want them to be able to easily find the video on your channel (or be recommended the video in their Youtube homepage) you should still publish the video as "Public" (the "visibility" setting), even if you uncheck the "publish to subscriptions feed".

These are two different settings.

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