  The effects induced by the time-reversal ($\mathcal{T}$) and spatial parity
($\mathcal{P}$) violating electron-nucleus and electron-electron interactions
mediated by the axion-like particles (ALPs) in the BaF molecule were estimated.
Molecular parameters characterizing these interactions were calculated across a
wide range of ALP masses. In case of the electron-nuclear interaction, the
effect of the extended nucleus was studied and shown to be significant for
heavy ALPs. Based on the calculated molecular parameters, we obtained a link
between the $\mathcal{T}$,$\mathcal{P}$-violating energy shift which can be
measured in the ongoing experiment designed to search for the electron electric
dipole moment using the BaF molecule [A. Boeschoten et al., arXiv:2303.06402
(2023)] and the products of coupling constants of the ALP-electron or
ALP-electron and ALP-nucleus interactions.
