I hear you @orange-assistant, so I will run some tests, when the next ESPHome update is available. One with and one without that setting enabled, I’ll be corious to see, what’s happening. 
It’s hard to test it right now, without an update available, because I have all my devices updated (as usual) right after the last update from ESPHome (Add-on).
@stevemann Click on that firmware entity in the screen I posted the pic from above. In the popup opened, click on the cogwheel (right top corner, second from right).
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GROK
(Finally).
Standing in the forest and looking for a tree. I finally realized that the Firmware is an entity of the device, and this disables the Firmware entity for this device. If there is no entity, there’s nothing to update.
Many thanks for your patience- both of you.
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So the new ESPHome update for this month has just arrived, and I wanted to test that a little.
@orange-assistant
Any specific ideas on what to test? I’d do this way, but am open to all ideas:
- Disable two of the “firmware” entities for two ESPHome devices
- Install new ESPHome Add-on version
- Check which devices are listed under repairs
- Report back
Anything I’m missing?
No that should do it. The two you disable should not generate update notifications.
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Here we go with the confirmation of the above stated! 
If you disable the firmware entity of that device, it will not be listed under the devices to update in the system settings.
So this is the solution, if you don’t want to be notified about an update of that specific entity (see the pic):