Disclaimer: I'm not a native speaker so my grammar may be off.
I think it's called Spivak pronouns?

It's a gender-neutral pronoun, that goes like this:
he, she – e
him, her – em
his, her – eir
his, hers – eirs

It's one of many inventions to replace 'he' and 'she' in a gender-neutral
way. I myself am becoming more and more comfortable with just using the
singular 'they', but for a long time after playing Agora I was a proponent
of Spivak. Its advantage would be that it is clearly singular, while 'they'
might throw reader's off who only use it for plural. Of course, 'eir' also
throws off peole who haven't heard it before.

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