Henry VI Part III was probably written around 1591-92.

In a pamphlet of 1592 Shakespeare is famously described as 'an upstart crow, beautified with our feathers, that with his Tiger's heart wrapped in a player's hide, supposes he is well able to bombast out a blank verse as the best of you,' which references Margaret's line in Henry VI Part III.

There is no consensus as to whether the play was solely written by Shakespeare, and it was first published as a shorter version in Quarto in 1595.

Sources

As with the other parts of Henry VI, primary sources seem to include Edward Hall's The Union of the Two Noble and Illustre Famelies of Lancastre and Yorke (1548) and Holinshed's Chronicles.