  CEMP-no stars, a subset of carbon enhanced metal poor (CEMP) stars ($\rm
[C/Fe]\geq0.7$ and $\rm [Fe/H]\lesssim-1$) have been discovered in ultra-faint
dwarf (UFD) galaxies, with $M_{\rm vir} \sim 10^8$ Msun and
$M_{\ast}\sim10^3-10^4$ Msun at $z=0$, as well as in the halo of the Milky Way
(MW). These CEMP-no stars are local fossils that may reflect the properties of
the first (Pop~III) and second (Pop~II) generation of stars. However,
cosmological simulations have struggled to reproduce the observed level of
carbon enhancement of the known CEMP-no stars. Here we present new cosmological
hydrodynamic zoom-in simulations of isolated UFDs that achieve a gas mass
resolution of $m_{\rm gas}\sim60$ Msun. We include enrichment from Pop~III
faint supernovae (SNe), with $ E_{\rm SN}=0.6\times10^{51}$ erg, to understand
the origin of CEMP-no stars. We confirm that Pop~III and Pop~II stars are
mainly responsible for the formation of CEMP and C-normal stars respectively.
New to this study, we find that a majority of CEMP-no stars in the observed
UFDs and the MW halo can be explained by Pop~III SNe with normal explosion
energy ($ E_{\rm SN}=1.2\times10^{51}$~erg) and Pop~II enrichment, but faint
SNe might also be needed to produce CEMP-no stars with $\rm [C/Fe]\gtrsim2$,
corresponding to the absolute carbon abundance of $\rm A(C)\gtrsim6.0$.
Furthermore, we find that while we create CEMP-no stars with high carbon ratio
$\rm [C/Fe]\approx3-4$, by adopting faint SNe, it is still challenging to
reproduce CEMP-no stars with extreme level of carbon abundance of $\rm
A(C)\approx 7.0-7.5$, observed both in the MW halo and UFDs.
