My game suffer from problems with screen adaptation. I finally changed screen size and screenfilling to letterbox scale, but i understand, that it will be better, if UI will be over black boxes, not on the edge of black box. Is in possible to make it like that ?
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No, that's not possible as far as I know.
The most common solution is to change scaling mode to "Scale outer" and make the UI adjustable (say, using Anchor behavior).