Electronic device, protective case for electronic device, and displaying method thereof

A case, an electronic device and a method are disclosed herein. The case is mountable onto the electronic device. The electronic device includes a display, a first sensor, a second sensor different than the first sensor, a processor operatively connected with the display, the first sensor, and the second sensor, and a memory operatively connected with the processor. The processor implements the method, including: display a screen on the display, detect, by the first sensor, whether a first part of a detachable peripheral device is mounted on an outer portion of the electronic device, obtain, by the second sensor, information from a second part of the detachable peripheral device, when the second part is coupled to the first part, and when the first part is detected through the first sensor, and the information is obtained through the second sensor, execute a screen split mode dividing the screen into regions.