How to take small-sized-(~50KB) good quality screenshots using overlay button?
Touchshot is an app I use which has both you are looking for 


Hover button (overlay)
JPEG / PNG - JPEG quality 80 /90 /100 and resolution can be varied from 640 x 360 , 1280 x 720, 1920 x 1080


Minimum size by manipulating these is still around 100 kB and not as low as you want. There may be other apps that offer size you want but not with overlay function. As an additional feature , you get date and time stamped screenshots