CERN-LHC. This Letter presents the measurement of the fiducial and differential cross-sections of the electroweak production of a Zy pair in association with two jets. The analysis uses 140 fb-1 of LHC proton-proton collision data taken at sqrt(s)=13 TeV recorded by the ATLAS detector during the years 2015-2018. Events with a Z boson candidate decaying into either an e+e- or mu+mu- pair, a photon and two jets are selected. The electroweak component is extracted by requiring a large dijet invariant mass and a large rapidity gap between the two jets and is measured with an observed and expected significance well above five standard deviations. The fiducial pp-->Zyjj cross-section for the electroweak production is measured to be 3.6 +- 0.5 fb. The total fiducial cross-section that also includes contributions where the jets arise from strong interactions is measured to be 16.8+2.0-1.8 fb. The results are consistent with the Standard Model predictions. Differential cross-sections are also measured using the same events and are compared with parton-shower Monte Carlo simulations. Good agreement is observed between data and predictions. The cross section values reported in the tables has already been updated with the latest integrated luminosity for ATLAS full Run2 as well as the uncertainty on the global normalisation ("Lumi"). See doi:10.48550/ARXIV.2212.09379 for more details. The Signal fiducial region is defined as: - At least 2 leptons (ee or mumu) - abs(eta_lep) < 2.5 and leading lepton with pT > 30 GeV and second pT > 20 GeV. - At least 1 photon - Exclude photon with Delta_R(lep,gamma) < 0.4 - E_T^gamma > 25 GeV, abs(eta_gamma) < 2.37 - Photon Isolation: scalar sum of p_T for all stable particles (except nu, mu and the photon itself) within a cone of radius Delta_R=0.2 around the photon, E_T^cone20, less than 7% of photon p_T - At least 2 jets - Exclude jet with Delta_R(gamma,jet) < 0.4 or Delta_R(lep,jet) < 0.3 - p_T^j > 50 GeV, abs(rap_j) < 4.4 - Abs(Delta_rap(j1,j2)) > 1.0, no extra jet in rapidatity gap between the 2 leading jets - m_jj > 500 GeV - m_ll > 40 GeV - m_ll + m_llgamma > 182 GeV - Zy_centrality defined as | rap_Zgamma - (rap_j1 +rap_j2)/2 | / | rap_j1 - rap_j2 | < 0.4 The Extended Signal fiducial region is defined as: - Selections as Signal region but without m_jj selection - m_jj > 150 GeV The QCD Control fiducial region is defined as: - Selections as Signal region but without Zy_centrality selection - 5 > Zy_centrality > 0.4