Antiocha de Coggeshall

Per Wikipedia:

Hawkwood had two wives. Little is known of the first, except that she was probably English, and she gave birth to at least one child, a daughter named Antiochia, who married into a prominent English Essex family, the Coggeshales.[1]:13 Through her daughter Alice Coggeshall, Hawkwood is an ancestor of the Earls of Inchiquin.

https://en.wikipedia.org/wiki/John_Hawkwood

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Chronology requires that Antiocha (or Mary) Hawkwood was born before her father's marriage to Domnina Visconti. She might have been illegitimate. She was living in 1379 at Milan with her husband Sir William de Coggeshall, therefore she was already an adult in 1377 when her father married Domnina Visconti.

As the author rightly states on p. 47, the identity of Hawkwood's first wife is not yet known. However she does go further to speculate at the time of this marriage it is thought that Hawkwood was in the service of John de Vere in France (1350-1356). The fact that Hawkwood's daughter was named Antiocha suggests that Hawkwood's first wife may have been a de Vere to honor Robert de Vere's miracle of a bright star appearing on de Vere's shield while night fighting in the first Crusade at Antioch in 1098.

Hawkwood's son-in-law Sir William Coggleshall of Codham, Essex is mentioned as living for a period in Milan and also there is a mention of a bastard son of Hawkwood born 1353-1356 for whom Hawkwood was attempting to legitimate through the Pope.

No mention is made of the alleged daughter Beatrice.

As the Hawkwoods were from Sible Hedingham, Essex and the de Veres of Hedingham, Essex, the Hawkwood-de Vere marriage is a possibility, but remains unproved. Hawkwood has a six year absence from records from 1350 to 1356, but when he reappears in 1356 it is in the service of John de Vere, Earl of Oxford in France.

may have died in Milan, Milan, Lombardy, Italy