  We investigate how patchy reionization affects the star formation history
(SFH) and stellar metallicity of ultra-faint dwarf galaxies (UFDs). Patchy
reionization refers to varying ultraviolet (UV) background strengths depending
on a galaxy's environment. Recent observations highlight the significance of
this effect on UFDs, as UFDs can have different SFHs depending on their
relative position with respect to their host halo during the period of
reionization. However, most cosmological hydrodynamic simulations do not
consider environmental factors such as patchy reionization, and the effect of
reionization is typically applied homogeneously. Using a novel approach to
implement patchy reionization, we show how SFHs of simulated UFDs can change.
Our cosmological hydrodynamic zoom-in simulations focus on UFD analogs with
M_vir~10^9solar mass, M_star < 10^5 solar mass at $z=0$. We find that patchy
reionization can weaken the effect of reionization by two orders of magnitude
up to $z=3$, enabling late star formation in half of the simulated UFDs, with
quenching times $\sim$460 Myr later than those with homogeneous reionization.
We also show that halo merger and mass assembly can affect the SFHs of
simulated UFDs, in addition to patchy reionization. The average stellar
iron-to-hydrogen ratio, [Fe/H], of the simulated UFDs with patchy reionization
increases by 0.22-0.42 dex. Finally, our findings suggest that patchy
reionization could be responsible for the extended SFHs of Magellanic UFDs
compared to non-Magellanic UFDs.
