Cognate rings are accessories that Cognates wear on each of their thumbs when performing mind readings. Fitz gave Sophie a pair as a Midterms gift, which were engraved with their initials, SEF and FAV. When Cognates' minds are telepathically linked, the rings snap together, since the rings are made of a specific mineral used for Cognate Rings.
This is Proof of Fitz Love of Sophie (or Fitzphie)