Question: Who wrote the Beatles song that was released on the B-side of the single featured on the film soundtrack of the same name in 1964?

Context paragraphs:
Why Georgia: "Why Georgia" is the third single released by John Mayer from his first album, "Room for Squares".  As a B-side, the international version single featured the live version of "Why Georgia" as it appeared on Mayer's first live album, "Any Given Thursday," as the single followed the live album's release.  The international single was released only two months prior to Mayer's second album, "Heavier Things".

Things We Said Today: "Things We Said Today" is a song by English rock band the Beatles written by Paul McCartney and credited to Lennon–McCartney.  It was composed for the film "A Hard Day's Night" but was eventually not included.  It does appear on the soundtrack album.  It was also released as the B-side of the single "A Hard Day's Night" in the UK.

Blue Money: "Blue Money" is a song written by Northern Irish singer-songwriter Van Morrison.  It was the second of two Top Forty hits from his 1970 album, "His Band and the Street Choir" (the other being "Domino"), reaching #23 on the US charts.  The US single featured "Sweet Thing", from the album "Astral Weeks", as the B-side.  It was released as a single in the UK in June 1971 with a different B-side, "Call Me Up in Dreamland".  The song became Morrison's third best selling single of the 1970s, remaining on the charts for three months.

A Hard Day's Night (song): "A Hard Day's Night" is a song by the English rock band the Beatles.  Credited to Lennon–McCartney, it was written by John Lennon, with some collaboration from Paul McCartney.  It was released on the film soundtrack of the same name in 1964.  It was also released in the UK as a single, with "Things We Said Today" as its B-side.

Miles Away (Winger song): "Miles Away" is a song by American rock band Winger, from their album "In the Heart of the Young".  Released in late 1990 to pop radio after already reaching number one in most AOR markets, the song peaked at #12 on the Hot 100.  It is also significant for being Winger's only ever hit single in the United Kingdom, reaching #56 on 24 January 1991.  The song references "Just When I Needed You Most" by Randy Vanwarmer, another Colorado artist.  The single featured a B-side, "All I Ever Wanted", that was never released on any other Winger albums or compilations, though it did appear, in demo form, on the "Demo Anthology".

A New Day (song): "A New Day" is a non-album single by Killing Joke.  It was released by E.G. Records in July 1984 as a 12" and 7" single.  The 12" single featured a dub mix of "A New Day" as the A-side and "A New Day" as the B-side.  The 7" single featured a shorter version of "A New Day" as the A-side and "Dance Day" as the B-side.  A completely different version of "A New Day", which was not a mix, later appeared on the 2008 reissue of Killing Joke's fifth studio album, "Night Time".  The single reached No. 51 in the UK Singles Chart.  A promotional video was filmed for the song, marking the first time the band had made a video for a non-album single.

Star (Stellar song): "Star" is New Zealand band Stellar's ninth single, and their third single from their second album Magic Line.  This single is the last of the band's to have a physical release.  The single, though charting for five weeks would only reach a position of #40.  The single featured two B-sides, the Sub Mariner Remix of Taken, as well as the new B-side We Go Out.  This song would later be featured on the soundtrack to the New Zealand horror film The Locals in 2003.  Furthermore.  after five minutes of silence the single would feature some bonus material.  The first bonus sound clip was of the song We Go Out being read by a speech synthesiser and the other being a short James Bond take-of, where Andrew Maclaren played the role of James Bond and Kurt Shanks the speaking role of Miss Moneypenny.

Me or You?: "Me or You?"  is the second non-album single by Killing Joke.  It was released by E.G. Records in October 1983 as a 12", 7", and a limited double vinyl 7" single.  The B-side for the 12" and 7" single featured "Feast of Blaze", originally from their fourth studio album, "Fire Dances".  However, only the 12" featured the track "Wilful Days" as a B-side.  The limited double vinyl 7" single featured "Wilful Days" as a C-side with a blank D-side.  Both "Wilful Days" and "Me or You?"  later appeared on the 2008 reissue of "Fire Dances", along with a John Peel session version of "Wilful Days".  The single reached No. 57 in the UK Singles Chart that same month.

Kings and Queens (Killing Joke song): "Kings and Queens" is Killing Joke's third single from their fifth studio album, "Night Time".  It was originally released by E.G. Records on 21 March 1985 as a 12" and 7" single in the UK, and a 7" single by Polydor in the Netherlands.  It was produced by Chris Kimsey.  The 12" single featured "Kings and Queens (A Right Royal Mix)" as an A-side, and both "The Madding Crowd (Remixed by Killing Joke)" and "Kings and Queens" as B-sides. E.G.'s 7" single and Polydor's 7" single exempted "Kings and Queens (A Right Royal Mix)" and instead featured "Kings and Queens" as the A-side, and "The Madding Crowd (Remixed by Killing Joke)" as the B-side.  E.G. also released a remix of the song, "Kings and Queens (Knaves Mix)", as an A-side and featured the same B-sides as the 12" single of "Kings and Queens".

Epitáfio: "Epitáfio" is the fifteenth single by Titãs, released in 2002.  It was included in the soundtrack of telenovela "Desejos de Mulher".  As a B-side, the single featured an acoustic version of the song.  Unlike the whole band, producer Jack Endino believed it could be a hit and was eventually proven right.

Supporting paragraphs: Things We Said Today A Hard Day's Night (song)
Answer: Paul McCartney