  We report 23 stars having Galactocentric velocities larger than
$450~\mathrm{km\,s}^{-1}$ in the final data release of the APOGEE survey. This
sample was generated using space velocities derived by complementing the high
quality radial velocities from the APOGEE project in Sloan Digital Sky Survey's
Data Release 17 (DR17) with distances and proper motions from Gaia early Data
Release 3 (eDR3). We analyze the observed kinematics and derived dynamics of
these stars, considering different potential models for the Galaxy. We find
that three stars could be unbound depending on the adopted potential, but in
general all of the stars show typical kinematics of halo stars. The APOGEE DR17
spectroscopic results and Gaia eDR3 photometry are used to assess the stellar
parameters and chemical properties of the stars. All of the stars belong to the
red giant branch, and, in general, they follow the abundance pattern of typical
halo stars. There are a few exceptions that would deserve further analysis
through high-resolution spectroscopy. In particular, we identify a high
velocity Carbon-Enhanced Metal-Poor (CEMP) star, with Galactocentric velocity
of 482 km\,s$^{-1}$. We do not confirm any hypervelocity star in the sample,
but this result is very sensitive to the adopted distances, and less sensitive
to the Galactic potential.
