The first observation of exotic states with a new quark content cc[over ¯]us[over ¯] 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, Z_{cs}(4000)^{+}, has a mass of 4003±6_{-14}^{+4} MeV, a width of 131±15±26 MeV, and spin parity J^{P}=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, Z_{cs}(4220)^{+} and X(4630), are observed with significance exceeding 5 standard deviations.