This paper presents a search for exotic decays of the Higgs boson into a pair of new pseudoscalar particles, 𝐻→𝑎⁢𝑎, where one pseudoscalar decays into a 𝑏-quark pair and the other decays into a 𝜏-lepton pair, in the mass range 12 ≤𝑚𝑎 ≤60  GeV. The analysis uses 𝑝⁢𝑝 collision data at √𝑠 =13  TeV collected with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 140  fb−1. No significant excess above the Standard Model (SM) prediction is observed. Assuming the SM Higgs boson production cross section, the search sets upper limits at 95% confidence level on the branching ratio of Higgs bosons decaying into 𝑏⁢¯𝑏⁢𝜏+⁢𝜏−, ℬ(𝐻 →𝑎⁢𝑎 →𝑏⁢¯𝑏⁢𝜏+⁢𝜏−), between 2.2% and 3.9% depending on the pseudoscalar mass.