Recent results from the proton-proton collision data taken by the ATLAS experiment
on the charmonium production and on the $B_c^+$ meson production and decays are presented. The measurement of $J/\psi$ meson and $\psi(2S)$ meson differential cross sections is reported.
New results on the $B_c^+$ meson decays to $J/\psi D_s^{(*)}$
final states are included. Both studies are based on $pp$ collision data
collected at $\sqrt{s}=13$ TeV during the LHC Run 2, corresponding to an integrated luminosity of
139 fb$^{-1}$.
The measurement of the differential ratios of the $B_c^+$ and $B^+$ mesons production cross sections at $\sqrt{s}=8$ TeV with an
integrated luminosity of 20.3 fb$^{-1}$ is also discussed.