  We report 75As-NMR/NQR results on new iron-arsenide compounds
(La0.5-xNa0.5+x)Fe2As2. The parent compound x=0 exhibits a stripe-type
antiferromagnetic (AFM) order below T_N=130 K. The measurement of nuclear spin
relaxation rate at hole-doped x=+0.3 and heavily electron-doped x=-0.5 revealed
that the normal-state properties are dominated by AFM spin fluctuations
(AFMSFs), which are more significant at x=+0.3 than at x=-0.5. Their
superconducting (SC) phases are characterized by unconventional multi-gap SC
state, where the smaller SC gaps are particularly weaken in common. The
experimental results indicate the close relationship between the AFMSFs and the
SC from the hole-doped state to heavily electron-doped state, which shed light
on a unique SC phase emerged in the heavily electron-doped regime being
formally equivalent to non-SC compound Ba(Fe0.5Co0.5)Fe2As2.
