from Proto-Italic*jougestos(“yoked”), from *jougos(“teamofyokeanimals”) (whenceLatiniūgerapl), from Proto-Indo-European*(H)yewg-es-, from *(H)yewg-(“join together”);
from Proto-Italic*jugistos(“closest”), equivalent to *(H)yug- + *-istHos(“superlative suffix”); however, this suffix is otherwise not found in Latin.
The accusative is from the suffix used adverbially.
Note: the length of the /u/ is uncertain due to lack of graphic attestations, unclear etymology and common conflation with iūstus(“just; exact”) already in Latin as well as its Romance descendants. Most other dictionaries list it as short.