  The origin of apparently young $\alpha$-rich stars in the Galaxy is still a
matter of debate in Galactic archaeology, whether they are genuinely young or
might be products of binary evolution and merger/mass accretion. We aim to shed
light on the nature of young $\alpha$-rich stars in the Milky Way by studying
their distribution in the Galaxy thanks to an unprecedented sample of giant
stars that cover different Galactic regions and have precise asteroseismic
ages, chemical, and kinematic measurements. We analyze a new sample of $\sim$
6000 stars with precise ages coming from asteroseismology. Our sample combines
the global asteroseismic parameters measured from light curves obtained by the
K2 mission with stellar parameters and chemical abundances obtained from APOGEE
DR17 and GALAH DR3, then cross-matched with Gaia DR3. We define our sample of
young $\alpha$-rich stars and study their chemical, kinematic, and age
properties. We investigate young $\alpha$-rich stars in different parts of the
Galaxy and we find that the fraction of young $\alpha$-rich stars remains
constant with respect to the number of high-$\alpha$ stars at $\sim$ 10%.
Furthermore, young $\alpha$-rich stars have kinematic and chemical properties
similar to high-$\alpha$ stars, except for [C/N] ratios. This suggests that
these stars are not genuinely young, but products of binary evolution and
merger/mass accretion. Under that assumption, we find the fraction of these
stars in the field to be similar to that found recently in clusters. This fact
suggests that $\sim$ 10% of the low-$\alpha$ field stars could also have their
ages underestimated by asteroseismology. This should be kept in mind when using
asteroseismic ages to interpret results in Galactic archaeology.
