There is no particular qualification in knee surgery itself. Most surgeons specialising in knee surgery are qualified in general orthopaedic surgery, and have gravititated towards specialising in knees.
In a superspeciality like this, it is highly regarded to do a 'fellowship' of one or two years with a mentor or orthopaedic unit specialising in knee surgery. Fellows often travel to other parts of the world to join a specialist unit like that.
In the USA a superspecialist is likely to have Board Certification in addition to having been involved in one or more Fellowships. Other countries may have superspecialist degrees of various kinds, eg in the UK there is Fellowship of the Royal College of Surgeons (FRCS).