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An analysis of the flavour structure of dimension-6 effective field theory (EFT) operators in multilepton final states is presented, focusing on the interactions of quarks with Z bosons. For the first time, the flavour structure of these operators is disentangled by simultaneously probing the interactions with different quark generations. The analysis targets the associated production of a top quark pair and a Z boson, as well as diboson processes in final states with at least three leptons, which can be electrons or muons. The data were recorded by the CMS experiment in the years 2016–2018 in proton-proton collisions at a centre-of-mass energy of 13 TeV and correspond to an integrated luminosity of 138 fb−1. Consistency with the standard model of particle physics is observed and limits are set on the selected Wilson coefficients, split into couplings to light- and heavy-quark generations.