Evidently an app you are using requires the accessibility service in order to be able to perform some function.

Why do you not want to use accessibility?
What do you think will happen if you do?

Although you probably want to keep apps using this service to a minimum, it is a requirement for some apps to use accessibility in order for certain features to work.

 

How do you know you have no use for it?

Obviously some app you have downloaded is requesting it, and you are missing out on whatever features that app can provide when it is allowed accessibility.

From the sound of your description, it seems to me that you are using Greenify or another app to close other apps when the screen goes off.

In order for this to function properly, you do indeed need to allow such an app accessibility.

From your homescreen (devices- and therefore pathways to these settings, and their names- may vary)...

Settings
Accessibility

Here you should see a headline of 'Services'.
These are the apps that you have downloaded that can use the accessibility service.

Below those are the built in system options that are also under the Accessibility area.

There are some neat things here, and now that you know where they are, you can explore them.

The next time you get the message (if it is Greenify, then it will appear when the screen awakens, or when you unlock the device) go into Accessibility and allow each app in turn (unless my guess is correct about it being Greenify- then just allow that), then replicate what you did before the message appeared.

Eventually you will allow the right one, and the message will cease.