An amplitude analysis of the B+→D+sD−sK+ decay is carried out to study for the first time its intermediate resonant contributions, using proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV. A near-threshold peaking structure, referred to as X(3960), is observed in the D+sD−s invariant-mass spectrum with significance greater than 12 standard deviations. The mass, width, and the quantum numbers of the structure are measured to be 3956±5±10 MeV, 43±13±8 MeV, and JPC=0++, respectively, where the first uncertainties are statistical and the second systematic. The properties of the new structure are consistent with recent theoretical predictions for a state composed of c¯cs¯s quarks. Evidence for an additional structure is found around 4140 MeV in the D+sD−s invariant mass, which might be caused either by a new resonance with the 0++ assignment or by a J/ψϕ↔D+sD−s coupled-channel effect.Received 28 October 2022Revised 6 February 2023Accepted 28 February 2023DOI:https://doi.org/10.1103/PhysRevLett.131.071901Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.© 2023 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)Research AreasMultiquark bound statesParticle interactionsStrong interactionParticles & Fields