  The first observation of exotic states with a new quark content $c \bar{c} u
\bar{s}$ decaying to the $J/\psi K^+$ final state is reported with high
significance from an amplitude analysis of the $B^+ \to J/\psi \phi K^+$ 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 centre-of-mass energies of 7, 8 and 13 TeV. The most significant state,
$Z_{cs}(4000)^+$, has a mass of $4003\pm6\,^{+\,\phantom{0}4}_{-\,14}$ MeV, a
width of $131\pm15\pm26$ 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 $J/\psi \phi$ final state is also observed with
high significance. In addition, the four previously reported $J/\psi \phi$
states are confirmed and two more exotic states, $Z_{cs}(4220)^+$ and
$X(4630)$, are observed with significance exceeding five standard deviations.
