1. Apply a drop-shadow as in your second example.
 2. Go to the blending options for the drop-shadow effect.
 3. Tick the box which says: "Layer mask hides effects".

[![enter image description here][1]][1]

 4. You can now use selection tools to select the inner drop-shadow circle of your layer
 5. With this inner drop shadow selected, you can mask it out.

[![enter image description here][2]][2]

 6. Invert the mask, if necessary with <kbd>Ctrl / Cmd</kbd>+<kbd>i</kbd>

  [1]: https://i.sstatic.net/RgFYw.jpg
  [2]: https://i.sstatic.net/qfLLG.jpg