According to Wikipedia the song was copyrighted in 1835 by the American music publisher Charles Bradlee under the title "The A.B.C". The melody was attributed firstly to Louis Le Maire, an 18th century composer, then to Mozart.
Are there any known alternative mnemonic songs or chants for the alphabet, which predated 1835?
While you wait for further discussion from qualified experts, you may be interested in a previous response by /u/UrAccountabilibuddy to a similar question.
How did children learn the alphabet before the well-known ABC song was first copyrighted in 1835?