  We report on new flavor tagging algorithms developed to determine the
quark-flavor content of bottom ($B$) mesons at Belle II. The algorithms provide
essential inputs for measurements of quark-flavor mixing and charge-parity
violation. We validate and evaluate the performance of the algorithms using
hadronic $B$ decays with flavor-specific final states reconstructed in a data
set corresponding to an integrated luminosity of $62.8$ fb$^{-1}$, collected at
the $\Upsilon$(4$S$) resonance with the Belle II detector at the SuperKEKB
collider. We measure the total effective tagging efficiency to be
$\varepsilon_{\rm eff} = \big(30.0 \pm 1.2(\text{stat}) \pm
0.4(\text{syst})\big)\%$ for a category-based algorithm and $\varepsilon_{\rm
eff} = \big(28.8 \pm 1.2(\text{stat}) \pm 0.4(\text{syst})\big)\%$ for a
deep-learning-based algorithm.
