The name actually comes from "any". Amazing.
All known anyons are quasiparticles.
Key physical experiment: fractional quantum Hall effect.
Exotic and hard to find experimentally.
Topological quantum computation by Jason Alicea (2021)
Source. Articles by others on the same topic
An anyon is a two-dimensional quasiparticle whose exchange or braiding statistics can differ from bosonic and fermionic statistics.