Shimajiri dialect (the linguistic affiliations of the Shimajiri dialects are uncertain, but are often included in the Southern dialect because the Shimajiri region is often considered to be part of that region)
There is no universally-accepted concrete proof of the relationship between Japonic languages and other languages, but there are a variety of theories each backed up with a varying degree of scientific evidence.
Japonic languages are related to the extinct language of ancient Goguryeo in Korea. Some go further to include both Japonic and Goguryeo in a larger hypothetical language family called the Fuyu languages that would also include scarcely-attested extinct languages associated with ancient Fuyu and Baekje.
Japonic languages are related to modern Korean based primarily on near-identical grammar, but there is scarce lexical similarity between the two; supporters of the Fuyu languages theory generally do not include modern Korean as part of that family.
As far as lexical studies have shown, the modern living non-Japonic language with the closest lexical similarity to any of the Japonic languages is Uyghur, a Turkic language.
In the wake of these theories, some argue that the similarity between all these languages is merely a sprachbund, and that the attested similarities between some or all of these languages are simply the result of their cultures being close geographic neighbors on the Asian mainland over the course of millennia.