Eizo Shimabuku's style of Shorin ryu, Shobayashi or Chubu Shorin ryu, teaches with it a system of Jiujitsu called Eizan-Ryu, which Shimabuku adapted from one he learend from a Japanese master, name unknown to me.
Motobu Ryu contains perhaps the jigen ry jujitsu system as part of its teachings.
Other styles teach some parts of jiujitsu or aikijitsu -like arts, within the context of kata applications, origin either Japan, Chinese chin na, or native Okinawan tegumi wrestling.
Is or are there an Okinawan style of Jiujitsu as such?I don't know, but probably not, much Okinawan grappling is subsumed within tegumi or Okinawan sumo.
Origin of which is, legendarily, the Japanese warrior Tametomo.
Having said which, any system of classical or modern jiujitsu is very useful as an adjunct to Okinawan or other karatye or striking styles.Jiujitsu is itself, a very useful collection of principles and techniques to know.
One of the finest and most effective and complete systems of Jiujitsu , and most widely available worldwide from many good teachers, is the system devised in the late eighteen hundreds by one Dr. Jigoro Kano, oroiginally called Kano Jiujitsu, now known as Judo.
Many are unaware that the complete Kodokan Judo system includes many two and one one person kata, striking, kicking, parrying, and defenses against same plus weapons, in addition to throwing, holding, locking etc.
It may be useful here to point out that a number of Okinawan tenth dans in karate, also have dan rank in Judo, Shoshin Nagamine was one such.I will note that his style of Shorin ryu's footwork and stances are highly compatible with either judo or Aikido technique.With no change.
Other Okinawan masters had rank in sumo and in various systems of Jiujitsu, including Sokon Matsumura, founder of the Shorin ryu.I believe some high ranking Goju people such as Eiichi Miyazato wwere or are very high in Okinawan Judo circles as well.My first judo teacher was apprently under Miyazato in Judo, on Okinawa.
Most of your Shotokan big guns also had or have, in Japan, Judo
experience, at least from high school.
I think that overseas, at the highest levels, lots of karate people have grappling training as well, this is something we are getting to in the West as well.
In the Sixties and Seventies, many of the first karateka also started in judo or jiujitsu.This may be why emphasis on grapling bunkai of kata wasn't a big deal then, we were all judoka anyway.