The magnetic behavior of T$$^{*}$$
∗
-phase cuprates in the underdoped region has been studied through zero-field muon spin rotation/relaxation ($$\mu $$
μ
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$$_{1-x/2}$$
1
-
x
/
2
Eu$$_{1-x/2}$$
1
-
x
/
2
Sr$$_{x}$$
x
CuO$$_{4-y}$$
4
-
y
F$$_{y}$$
y
(LESCOF). For as-grown (AS) samples, the onset temperature for development of spin correlation is determined by $$\mu $$
μ
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$$_{2-x}$$
2
-
x
Sr$$_x$$
x
CuO$$_4$$
4
. However, the damping of spin precession in the $$\mu $$
μ
SR time spectra appears to be significant than in La$$_2$$
2
CuO$$_4$$
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.