The first observation of exotic states with a new quark content c¯cu¯s decaying to the J/ψK+ final state is reported with high significance from an amplitude analysis of the B+→J/ψϕK+ decay. The analysis is carried out using proton-proton collision data corresponding to a total integrated luminosity of 9 fb−1 collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV. The most significant state, Zcs(4000)+, has a mass of 4003±6+4−14 MeV, a width of 131±15±26 MeV, and spin parity JP=1+, where the quoted uncertainties are statistical and systematic, respectively. A new 1+ X(4685) state decaying to the J/ψϕ final state is also observed with high significance. In addition, the four previously reported J/ψϕ states are confirmed and two more exotic states, Zcs(4220)+ and X(4630), are observed with significance exceeding 5 standard deviations.