An amplitude analysis of the Ds1(2460)+→Ds+π+π- transition is performed simultaneously in B0→D-Ds+π+π-, B+→D¯0Ds+π+π-, and B0→D*-Ds+π+π- decays. The study is based on a data sample of proton-proton collisions recorded with the LHCb detector at centre-of-mass energies of s=7,8, and 13 TeV, corresponding to a total integrated luminosity of 9fb-1. A clear double-peak structure is observed in the m(π+π-) spectrum of the Ds1(2460)+→Ds+π+π- decay. The data can be described either with a model including f0500,f0980, and f2(1270) resonances, in which the contributions of f0(980) and f2(1270) are unexpectedly large, or with a model including f0(500), a doubly charged open-charm tetraquark state Tcs¯++ and its isospin partner Tcs¯0. If the former is considered implausible, the Tcs¯ states are observed with high significance, and the data are consistent with isospin symmetry. When imposing isospin constraints between the two Tcs¯ states, their mass and width are determined to be (2327±13±13) MeV and (96±16-23+170) MeV, respectively, where the first uncertainty is statistical and the second is systematic. The mass is slightly below the DK threshold, and a spin-parity of 0+ is favoured with high significance.