Star formation in high-redshift dwarf galaxies is a key to understand early galaxy evolution in the early Universe. Using the three-dimensional hydrodynamics code GIZMO, we study the formation mechanism of cold, high-density gas clouds in interacting dwarf galaxies with halo masses of $sim 3 times 10^{7}~M_{odot}$, which are likely to be the formation sites of early star clusters. Our simulations can resolve both the structure of interstellar medium on small scales of $lesssim 0.1$ pc and the galactic disk simultaneously. We find that the cold gas clouds form in the post-shock region via thermal instability due to metal-line cooling, when the cooling time is shorter than the galactic dynamical time. The mass function of cold clouds shows almost a power-law initially with an upper limit of thermally unstable scale. We find that some clouds merge into more massive ones with $gtrsim 10^{4}~M_{odot}$ within $sim 2~{rm Myr}$. Only the massive cold clouds with $gtrsim 10^{3}~M_{odot}$ can keep collapsing due to gravitational instability, resulting in the formation of star clusters. In addition, we investigate the dependence of cloud mass function on metallicity and ${rm H_{2}}$ abundance, and show that the cases with low metallicities ($lesssim 10^{-2}~Z_{odot}$) or high ${rm H_{2}}$ abundance ($gtrsim 10^{-3}$) cannot form massive cold clouds with $gtrsim 10^{3}~M_{odot}$.
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