What was the first song to be penned and recorded by the Beatles?

Question

And who wrote it?

Answer 1

First penned would be by Harrison and Lennon, "Cry for a Shadow" 1961 but was not published until the Anthology I

First penned and recorded would be "I Want To Hold Your Hand" by Lennon/McCartney 1963

Answer 2

Was it "The One After 909"?

1957 by Lennon-McCartney, but not recorded til 1970

Answer 3

Hello

  I believe it was I Wanna Hold Your Hand  around 1962 or 63 Before they came to America  John Lennon wrote the song