If we use sibling-based terminology, we can come up with quarter sibling (as we have full sibling, half-sibling and three-quarter sibling).
(Note: It would be a colloquial (or even jocular) coinage rather than biological. Identical twins share 100% of their DNA, full siblings share 50% on average, three-quarter siblings share 37.5% on average and half-siblings share 25% on average. I think we can only go below 25% by leaving the realm of siblinghood and stepping into the realm of cousinhood; as first cousins share around 12,5% of their DNA. Thus, quarter sibling seems not to be applicable to biology.)
Urbandictionary defines quarter brother:
my half-brother's half-brother
Jason and Lydia's son is Sam. Clai and Lydia's son is Will. Jason and Maureen's son is Davis. Will and Davis are quarter brothers.
and quarter sister:
The half sister of my half sister or half brother.
Amy and Randy had Josie. Randy and Patty had Vanna. Patty and Bob had Andy.
Vanna is Josie's half sister.
Vanna is Andy's half sister.
Josie is Andy's quarter sister.
Andy is Josie's quarter brother.
However, the following excerpt got me thinking...
But if A is half sibling to B and B is half sibling to C, A can have virtually any relationship to C, with quarter sibling being among the least likely. Social relationships may not be based on such objectively measurable unidimensional scales as weight and size, nor even such indirectly measurable attributes as strength or "confidence."
Behavior, conservation, and ecology, Volume 2 by G. Mitchell, Joseph Erwin, Daris Ray Swindler
nonsibling: (biology) Any individual that is not a sibling [Wiktionary]