This paper presents a measurement of the electroweak production of twojets in association with a Z gamma pair, with the Z boson decaying intotwo neutrinos. It also presents a search for invisible or partiallyinvisible decays of a Higgs boson with a mass of 125 GeV producedthrough vectorboson fusion with a photon in the final state. Theseresults use data from LHC proton-proton collisions at root s = 13 TeVcollected with the ATLAS detector and corresponding to an integatedluminosity of 139 fb(-1). The event signature, shared by all benchmarkprocesses considered for the measurements and searches, is characterizedby a significant amount of unbalanced transverse momentum and a photonin the final state, in addition to a pair of forward jets. Electroweak Zgamma production in association with two jets is observed in this finalstate with a significance of 5.2 (5.1 expected) standard deviations. Themeasured fiducial cross-section for this process is 1.31 +/- 0.29 fb. Anobserved (expected) upper limit of 0.37 (0.34(-0.10)(+0.15)) at 95\%confidence level is set on the branching ratio of a 125 GeV Higgs bosonto invisible particles, assuming the Standard Model productioncross-section. The signature is also interpreted in the context ofdecays of a Higgs boson into a photon and a dark photon. An observed(expected) 95\% CL upper limit on the branching ratio for this decay isset at 0.018 (0.017(-0.005)(+0.007)), assuming the Standard Modelproduction cross-section for a 125 GeV Higgs boson.