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cryptophasia

n. The development by twins (identical or fraternal) of a language that only they can understand.

Wikipedia
Cryptophasia

Cryptophasia is a phenomenon of a language developed by twins (identical or fraternal) that only the two children could understand. The word has its roots from crypto meaning secret and phasia meaning speech. Most linguists associate cryptophasia with idioglossia, which is any language used by only one, or very few, people. Cryptophasia also differs from idioglossia on including mirrored actions like twin-walk and identical mannerisms.

While sources claim that twins and children from multiple births develop this ability perhaps because of more interpersonal communication between themselves than with the parents, there is inadequate scientific proof to verify these claims.