An accessory apparatus and an information display method are provided. The accessory apparatus include a housing, a display exposed through a first portion of the housing, a conductive pattern, a wireless communication circuit configured to support a short-range wireless communication protocol, at least one processor, and a memory, wherein the memory stores instructions that allow the at least one processor to control the wireless communication circuit to operate in the first mode, operate in the second mode in which the second type of external electronic device is allowed to read the second data for the second time period following the first time period, detect the existence of the second type of external electronic device at one or more points of time in the first time period, and switch into the second mode when the existence of the second type of external electronic device is detected.