  One class of competitive candidates for dark matter is ultralight bosons. If
they exist, these bosons may form long-lived bosonic clouds surrounding
rotating black holes via superradiant instabilities, acting as sources of
gravity and affecting the propagation of gravitational waves around the host
black hole. During extreme-mass-ratio inspirals, the bosonic clouds will
survive the inspiral phase and can affect the quasinormal-mode frequencies of
the perturbed black-hole-bosonic-cloud system. In this work, we compute the
shifts of gravitational quasinormal-mode frequencies of a rotating black hole
due to the presence of a surrounding bosonic cloud. We then perform a mock
analysis on simulated Laser Interferometer Space Antenna observational data
containing injected ringdown signals from supermassive black holes with and
without a bosonic cloud. We find that with less than an hour of observational
data of the ringdown phase of nearby supermassive black holes such as
Sagittarius A* and M32, we can rule out or confirm the existence of
cloud-forming ultralight bosons of mass $ \sim 10^{-17} \rm eV$.
