The Brief: Ae/aer and fae/faer pronouns are variations of gender-neutral third person pronouns.

DEEP DIVE
Ae/aer and fae/faer pronouns are gender-neutral third person pronouns. They are considered neopronouns as they fall outside of the more commonly known he/him/his, she/her/hers, and they/them/theirs.
As outlined by North Dakota State University, (f)aer and its forms can be used with or without the (F). For example, ae/aer/aers or fae/faer/faers.
According to the LGBTA Wikia, these pronouns were created in 1920 by a novelist David Lindsay to refer to an alien race, which were born from air and of a third sex.
Pronunciation
Ae is pronounced as “ay” and aer as “air,” according to University of Connecticut’s Rainbow Center.
Usage

More Pronouns
Other commonly used gender-neutral pronouns include: Ze/zir/zem/zeir, Xe/Xir/Xem/Xeir, and hir/hirself. Trans individuals sometimes use binary or non-binary pronouns, depending on how they identify their gender.