  We present a study of $\Xi_{c}^{0}\to\Xi^{0}\pi^{0}$,
$\Xi_{c}^{0}\to\Xi^{0}\eta$, and $\Xi_{c}^{0}\to\Xi^{0}\eta^{\prime}$ decays
using the Belle and Belle~II data samples, which have integrated luminosities
of 980~$\mathrm{fb}^{-1}$ and 426~$\mathrm{fb}^{-1}$, respectively. We measure
the following relative branching fractions $${\cal
B}(\Xi_{c}^{0}\to\Xi^{0}\pi^{0})/{\cal B}(\Xi_{c}^{0}\to\Xi^{-}\pi^{+}) = 0.48
\pm 0.02 ({\rm stat}) \pm 0.03 ({\rm syst}) ,$$ $${\cal
B}(\Xi_{c}^{0}\to\Xi^{0}\eta)/{\cal B}(\Xi_{c}^{0}\to\Xi^{-}\pi^{+}) = 0.11 \pm
0.01 ({\rm stat}) \pm 0.01 ({\rm syst}) ,$$ $${\cal
B}(\Xi_{c}^{0}\to\Xi^{0}\eta^{\prime})/{\cal B}(\Xi_{c}^{0}\to\Xi^{-}\pi^{+}) =
0.08 \pm 0.02 ({\rm stat}) \pm 0.01 ({\rm syst}) $$ for the first time, where
the uncertainties are statistical ($\rm stat$) and systematic ($\rm syst$). By
multiplying by the branching fraction of the normalization mode, ${\mathcal
B}(\Xi_{c}^{0}\to\Xi^{-}\pi^{+})$, we obtain the following absolute branching
fraction results $(6.9 \pm 0.3 ({\rm stat}) \pm 0.5 ({\rm syst}) \pm 1.3 ({\rm
norm})) \times 10^{-3}$, $(1.6 \pm 0.2 ({\rm stat}) \pm 0.2 ({\rm syst}) \pm
0.3 ({\rm norm})) \times 10^{-3}$, and $(1.2 \pm 0.3 ({\rm stat}) \pm 0.1 ({\rm
syst}) \pm 0.2 ({\rm norm})) \times 10^{-3}$, for $\Xi_{c}^{0}$ decays to
$\Xi^{0}\pi^{0}$, $\Xi^{0}\eta$, and $\Xi^{0}\eta^{\prime}$ final states,
respectively. The third errors are from the uncertainty on ${\mathcal
B}(\Xi_{c}^{0}\to\Xi^{-}\pi^{+})$. The asymmetry parameter for
$\Xi_{c}^{0}\to\Xi^{0}\pi^{0}$ is measured to be
$\alpha(\Xi_{c}^{0}\to\Xi^{0}\pi^{0}) = -0.90\pm0.15({\rm stat})\pm0.23({\rm
syst})$.
