Searches for Higgs and Z bosons decaying to an ฯ‰ meson and a photon, and for Higgs bosons decaying to a K(^โˆ—) and a photon are discussed using proton collision data recorded by the ATLAS experiment at โˆšs = 13 TeV between 2016 and 2018. The observed events are consistent with the expected background. The obtained 95% confidence level upper limit on the branching ratio for the H โ†’ ฯ‰ฮณ decay using 89.5 fb(^{โˆ’1}) of data is 1.0 ร—10(^{โˆ’4}) assuming a Standard Model Higgs Boson production. The analogous limit obtained for the Z โ†’ ฯ‰ฮณ decay is 3.5 ร—10({โˆ’7}). The obtained upper limit for the H โ†’ K(^โˆ—)ฮณ decay is 8.9 ร—10(^{โˆ’5}), using 134 fb(^{โˆ’1}) of data. The search for H โ†’ K(^โˆ—)ฮณ represents the first search for a flavour-violating exclusive decay of the Higgs boson.