Invented language, often between twins

Wikipedia Word definitions in Wikipedia
An idioglossia is an idiosyncratic language invented and spoken by only one person or very few people. Most often, idioglossia refers to the "private languages" of young children, especially twins , the latter being more specifically known as cryptophasia ...

Wiktionary Word definitions in Wiktionary
n. (context linguistics English) An invented form of dialect, language, or speech used by children, typically twins, and intelligible only to its speakers.