  We study the gravitational fragmentation of circumstellar discs accreting
extremely metal-poor ($Z \leq 10^{-3}$ Zsun) gas, performing a suite of
three-dimensional hydrodynamic simulations using the adaptive mesh refinement
code Enzo. We systematically follow the long-term evolution for 2000 years
after the first protostar's birth, for the cases of $Z = 0$, $10^{-5}$,
$10^{-4}$, and $10^{-3}$ Zsun. We show that evolution of number of
self-gravitating clumps qualitatively changes with $Z$. Vigorous fragmentation
induced by dust cooling occurs in the metal-poor cases, temporarily providing
about 10 self-gravitating clumps at $Z = 10^{-5}$ and $10^{-4}$ Zsun. However,
we also show that the fragmentation is a very sporadic process; after an early
episode of the fragmentation, the number of clumps continuously decreases as
they merge away in these cases. The vigorous fragmentation tends to occur later
with the higher $Z$, reflecting that the dust-induced fragmentation is most
efficient at the lower density. At $Z = 10^{-3}$ Zsun, as a result, the clump
number stays smallest until the disc fragmentation starts in a late stage. We
also show that the clump mass distribution also depends on the metallicity. A
single or binary clump substantially more massive than the others appear only
at $Z = 10^{-3}$ Zsun, whereas they are more evenly distributed in mass at the
lower metallicities. We suggest that the disc fragmentation should provide the
stellar multiple systems, but their properties drastically change with a tiny
amount of metals.
