Archaeopronouns are third person pronouns and forms or pronouns that were used in the past and are no longer in usage. However, some non-binary people may reclaim them and use these pronouns to express their gender in language. Most archaeopronouns are not found in the english language.
One example can be Classical Chinese pronoun "其", used by some Chinese non-binary people.
List of archaeopronouns in various languages
Chinese
伊 - used historically in 1870-1930 as an exclusively feminine pronoun.
渠
彼
其 - pronoun used in Classical Chinese
Old English
hē/hine/his - Old English masculine pronoun
hēo/hīe/hiere - Old English feminine pronoun
hit/hit/his - Old English neutral pronoun
Old Irish
dó/ind/and/fris - neutral & masculine
dí/inte/inde/friae - feminine
Resources
https://people.umass.edu/sharris/in/gram/GrammarBook/GramPersPronouns.html