Few-mode erbium-doped fiber amplifier (FM-EDFA) is a necessary repeater for long-haul mode division multiplexing (MDM) optical fiber communication systems, and its differential modal gain (DMG) directly affects the communication quality of the systems. In order to realize the gain equalization of different modes in FM-EDFA, a layered erbium ion doped ring core fiber supporting 4-mode group in cladding-pumped condition is proposed, and the pump mode is not considered. The ring core fiber is designed, and the DMG is reduced by controlling the change of the mode distribution induced by the central recess and outer groove refractive index of the core, combining with the well-designed doping radius and concentration of erbium ion. The results show that when erbium ions are doped in double layers in the ring core, the maximum DMG is reduced from 0.8 dB (single layer and uniform doping) to 0.44 dB (double layers in the ring core). In the full C band (1530--1565 nm), the gain of the 4-mode group is higher than 22 dB, the maximum DMG is less than 0.45 dB, and the noise figure is less than 5.3 dB. The cladding pump structure is conducive to the realization of all-fiber connection of FM-EDFA, is easy to integrate with MDM communication system, and gives full play to the all-optical compensation advantages of erbium-doped fiber amplifiers.