Atrinary or aternary: abinary genders that are completely unrelated to the gender trinary (such as quoigender, maverique, some aporagenders or most xenogenders). 

While abinary encompasses agender and neutrois (null-gender,

genderless, neutral-ningender, gender-free or gendervoid) and nonbinary includes androgyne, atrinary people have gender(s) that are completely removed from the concept of masculinity/femininity/neutrality/genderlessness/androgyny or (fe)male/neutrois/agender.

-Kau