The earliest printed version extant and probably ever is held by the British Library which lists it as: Barbara Allen's cruelty; or, the young-man's tragedy etc. [A ballad.]
There are numerous later editions including "Barbara Allen. Two-part song" arranged by Laurence Ager and published by Boosey & Hawkes of London in 1951 as part of Boosey's modern Festival Series; no. 161.
Alexander Baron - London, England, for above 3