This paper deals with design and refinement criteria of erbium doped hole-assisted optical fiber amplifiers for applications in the third band of fiber optical communication. The amplifier performance is simulated via a model which takes into account the ion population rate equations and the optical power propagation. The electromagnetic field profile of the propagating modes is carried out by a finite element method solver. The effects of the number of cladding air holes on the amplifier performance are investigated. To this aim, four different erbium doped hole-assisted lightguide fiber amplifiers having a different number of cladding air holes are designed and compared. The simulated optimal gain, optimal length, and optimal noise fig. are discussed. The numerical results highlight that, by increasing the number of air holes, the gain can be improved, thus obtaining a shorter amplifier length. For the erbium concentration NEr=1.8x1024 ions/m3, the optimal gain G(Lopt) increases up to ~2dB by increasing the number of the air holes from M=4 to M=10.