At this time disabling in-app notifications isn't possible. The reason behind this is that these notifications are used by our internal teams to communicate important or relevant information and changes to the Retail App and your account with you.
I recommend you submit a Feature Request here. This will help our product team get visibility and track other Sellers with similar interest in your request.
Important: When submitting a request, make sure to include the desired feature, and provide the details of how this feature will help your business succeed (how would you use it and what you expect from it).
JJ
Community Moderator, Square
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