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A4 is a size for printing. what matters is your document pixel dimension. it should be match with your displays resolution to fit perfectly. So, for example if you have a 1920x1080 screen resolution(very common nowadays), make the image according to that. If you are not sure about your screen, right click on desktop and choose some display option(depending on your operation system).
right click your desktop wallpaper and select screen resolution and put it on the highest numbers available which should be your true size settings. It sounds like you have a lower resolution than what your screens native resolution is if after you have applied that your A4 is slightly smaller than actual size then decrease the resolution until it matches.