  Let $n\in\mathbb{N}$ and ${\alpha}\in(0,\min\{2,n\})$. For any
$a\in[a^\ast,\infty)$, the fractional Schr\"odinger operator $L_\alpha$ is
defined by \begin{equation*}
L_\alpha:=(-\Delta)^{{\alpha}/2}+a{|x|}^{-{\alpha}}, \end{equation*} where
$a^*:=-{\frac{2^{\alpha}{\Gamma}((d+{\alpha})/4)^2}{{\Gamma}((d-{\alpha})/4)^2}}$.
Let $\gamma\in[0,\frac{\alpha}{n})$. In this paper, we introduce the VMO-type
spaces $\mathrm{VMO}_{L_\alpha}^\gamma (\mathbb{R}^{n})$ associated with
$L_\alpha$, and characterize these spaces via some tent spaces. We also prove
that, for any given $p\in(\frac{n}{n+\alpha},1]$, the space
$\mathrm{VMO}_{L_\alpha}^{\frac{1}{p}-1} (\mathbb{R}^{n})$ is the predual space
of the Hardy space $H_{L_\alpha}^p\left(\mathbb{R}^{n}\right)$ related to
$L_\alpha$.
