What is the name of strange fruit discovered in pastry nursery rhyme?

The nursery rhyme you are referring to is "Sing a Song of Sixpence". The strange fruit mentioned in this rhyme is a blackbird pie.

The full verse is:

"Sing a song of sixpence, a pocket full of rye,

Four and twenty blackbirds baked in a pie.

When the pie was opened the birds began to sing,

Was not that a dainty dish to set before the king?"

It's a rather unusual and humorous image, as blackbirds are not typically eaten!