Anontrinary or Anonternary is a gender that isn't trinary/ternary, but even still, is outside of non-trinary/non-ternary. It uses the prefix a- to show this, although it is not necessarily the same as agender. The difference being that agender is the lack of any gender. Anontrinary people have a feeling of gender, but that gender is not a trinary or non-trinary gender. Anontrinary can be a gender identity on it's own or it can be used as an umbrella term. Some anontrinary people may also identify as transgender.
Anontrinary can include genders (such as xenogenders) that aren't defined how they relate or don't relate to the gender trinary.
Anontrinary people can have any sexual orientation.