  We present the high-$z$ quasar candidate archive (HzQCA), summarizing the
spectroscopic observations of 174 $z\gtrsim5$ quasar candidates using
Keck/LRIS, Keck/MOSFIRE, and Keck/NIRES. We identify 7 candidates as $z\sim 6$
quasars 3 of them newly reported here, and 51 candidates as brown dwarfs. In
the remaining sources, 74 candidates are unlikely to be quasars; 2 sources are
inconclusive; the others could not be fully reduced or extracted. Based on the
classifications we investigate the distributions of quasars and contaminants in
color space with photometry measurements from DELS ($z$), VIKING/UKIDSS
($YJHK_s$/$YJHK$), and un\textit{WISE} ($W1W2$). We find that the identified
brown dwarfs are not fully consistent with the empirical brown dwarf model that
is commonly used in quasar candidate selection methods. To refine spectroscopic
confirmation strategies, we simulate synthetic spectroscopy of high-$z$ quasars
and contaminants for all three instruments. The simulations utilize the
spectroscopic data in HzQCA. We predict the required exposure times for quasar
confirmation and propose and optimal strategy for spectroscopic follow-up
observations. For example, we demonstrate that we can identify a $m_J=21.5$ at
$z=7.6$ or a $m_J=23.0$ at $z=7.0$ within 15\,min of exposure time with LRIS.
With the publication of the HzQCA we aim to provide guidance for future quasar
surveys and candidate classification.
