specific email notifications
Emulate the VIP concept in Apple mail to be able to be notified by messages that fall into that category only. So to have the ability to selectively be notified triggered by specific senders only. Notifications for every email is not helpful.

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Chris Brooking commented
The suggestion https://protonmail.uservoice.com/forums/284483-proton-mail/suggestions/33848425-filter-notifications expands on this
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Josh commented
I totally agree here. While Patrick's solution below is doable, that seems like a lot of heavy lifting to create a workaround for a feature that's available on most email clients.
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Daniel commented
I was going to suggest something similar, and the search of existing ideas shows me this one, including a few others (maybe https://protonmail.uservoice.com/forums/284483-proton-mail/suggestions/46653178-specific-email-notifications seems closest, but the year 2018 doesn't give me much hope at this point).
I hope Proton will join these similar suggestions+votes into one...
Anyhow, the first simple solution would be: selective notifications (on the phone) for only emails that are sent directly to you (i.e. excluding newsletters, certain forum notifications, e-shop ads, etc.).
An upgrade to this could be a setting where you choose categories/labels that notify you. -
Patrick commented
I've worked out a solution to this by forcing myself to get organised by adding filters to move messages not of interest to go to folders where notifications can be disabled.