The magnetic behavior of T \(^{*}\) -phase cuprates in the underdoped region has been studied through zero-field muon spin rotation/relaxation ( \(\mu \) SR) measurements. By examining the manner in which the superconducting transition temperature changes with increased fluorine substitution, we demonstrate the possibility of achieving an underdoped region in T \(^{*}\) -La \(_{1-x/2}\) Eu \(_{1-x/2}\) Sr \(_{x}\) CuO \(_{4-y}\) F \(_{y}\) (LESCOF). For as-grown (AS) samples, the onset temperature for development of spin correlation is determined by \(\mu \) SR measurement. We observed a substantial enhancement from \(\sim \) 7 K (x = 0.18, y = 0) to \(\sim \) 80 K (x = 0.18, y = 0.15) with an appearance of a magnetic order below \(\sim \) 55 K. Thus, the magnetic order can be stabilized by underdoping in AS T \(^{*}\) -LESCOF, similar to T-phase La \(_{2-x}\) Sr \(_x\) CuO \(_4\) . However, the damping of spin precession in the \(\mu \) SR time spectra appears to be significant than in La \(_2\) CuO \(_4\) (LCO), suggesting the presence of inhomogeneous magnetism. In addition, the unrecovered normalized time spectrum to 1/3 along the time axis indicates a dynamical nature of magnetism. These magnetic behavior disappears with oxidation annealing, even in the lightly hole-doped sample. The absence of static magnetism in the oxidation-annealed T \(^{*}\) -LESCOF could be attributed to the structural effect, as the physical properties of the T \(^{\prime }\) -phase cuprates has been discussed in terms of oxygen coordination around the Cu ion.