A colloquial particle indicating hearsay or uncertainty about reported information (equivalent to '...or so', '...or something', 'they say...').
彼は明日来るとやら、詳しいことはまだ聞いていない。
Apparently he's coming tomorrow, but I haven't heard the details yet.
あの店は安くて美味しいとやらで、いつも行列ができている。
That shop is supposedly cheap and tasty, so there's always a line.
彼女が留学することになったとやら、本当ならおめでたい話だ。
I hear she is going to study abroad; if true, that's wonderful news.