To screenshot using the apple logo at the back of my iphone, you will need to make sure that your iphone is on the new iOS 14 software update or higher.
In order to turn on the back feature,
1. Go to settings
2. Scroll down and tap "Accessibility" and then click "Touch".
3. Then scroll down to "Back Tap", this will give you the options to turn on "Double Tap" or "Triple Tap". Whichever you select gives you the same options next.
4. Click to see which features you can now control with either a double or triple tap on the Apple logo on the back of your iphone.
5. These options include taking screenshots, turning the volume up or down, magnifying, scrolling and more. For example, if you wanted to use a Double Tap to take screenshots, click the "Double Tap" option and then tick "Screenshot".
6. Now once that has been done, you should be able to take a screenshot just by tapping the Apple logo on the back of your phone twice.
NOTE: This feature might not work if you have a thick phone case, Also you can switch the features Back Tap controls or turn it off anytime by using the same steps above.
Let me know if you were able to do this on your iphone.