  We perform SubHalo Abundance Matching (SHAM) studies on UNIT simulations with
\{$\sigma, V_{\rm ceil}, v_{\rm smear}$\}-SHAM and \{$\sigma, V_{\rm
ceil},f_{\rm sat}$\}-SHAM. They are designed to reproduce the clustering on
5--30$\,\hmpc$ of Luminous Red Galaxies (LRGs), Emission Line Galaxies (ELGs)
and Quasi-Stellar Objects (QSOs) at $0.4<z<3.5$ from DESI One Percent Survey.
$V_{\rm ceil}$ is the incompleteness of the massive host (sub)haloes and is the
key to the generalized SHAM. $v_{\rm smear}$ models the clustering effect of
redshift uncertainties, providing measurments consistent with those from repeat
observations. A free satellite fraction $f_{\rm sat}$ is necessary to reproduce
the clustering of ELGs. We find ELGs present a more complex galaxy--halo mass
relation than LRGs reflected in their weak constraints on $\sigma$. LRGs, QSOs
and ELGs show increasing $V_{\rm ceil}$ values, corresponding to the massive
galaxy incompleteness of LRGs, the quenched star formation of ELGs and the
quenched black hole accretion of QSOs. For LRGs, a Gaussian $v_{\rm smear}$
presents a better profile for sub-samples at redshift bins than a Lorentzian
profile used for other tracers. The impact of the statistical redshift
uncertainty on ELG clustering is negligible. The best-fitting satellite
fraction for DESI ELGs is around 4 per cent, lower than previous estimations
for ELGs. The mean halo mass log$_{10}(\langle M_{\rm vir}\rangle)$ in
$\Msun{}$ for LRGs, ELGs and QSOs are ${13.16\pm0.01}$, ${11.90\pm0.06}$ and
${12.66\pm0.45}$ respectively. Our generalized SHAM algorithms facilitate the
production of mult-tracer galaxy mocks for cosmological tests.
