“Ain’t She Sweet”, was originally composed by Jack Yellen, whom wrote the lyrics, and Milton Ager, whom wrote the music. Later it was re-recorded by Gene Austin, being the first song on his album “My Blue Haven (Original Recordings 1927 – 1934”). The Beatles recorded their rock rendition of it on June 22, 1961 as the backing band for Tony Sheridan and was released on May 29, 1964 as a single, it as well appears on Anthology 1.
The song was re-recorded in 1969 during a jam session at Abbey Road Studios, this time with Ringo Starr as the drummer instead of Pete Best. The 1969 version appears on Anthology 3. According to Wikipedia, it is the only song to appear on two of the three Anthology records.