Birth of Henry Plantagenet at Hatfield
At the time of his birth, his parents had already two daughters, Joan (1438), who had also died in infancy, and Anne (10 August 1439). Their next son, Edward, was born on 28 April 1442. He was to accede the throne as Edward IV on 4 March 1461.
Unfortunately it is not sure whether he was born at Hatfield in Hertfordshire or Hatfield Chase in Yorkshire. Hatfield in Hertfordshire belonged to the Bishops of Ely, which is why it also called Bishops Hatfield. Their manor might have offered suitable accommodation on the way to London. The Great North Road connecting London and York ran through Hatfield.
Hatfield Chase was a royal hunting ground and one of the Duke of York’s family residences.  There are several sources linking Henry to this Hatfield. 
1. Michael K Jones, Bosworth 1485: Psychology of a Battle. Tempus, 2003, p.81
2. For instance: Jones, ibid.
S Whaley, The History and Antiquities of Thorne, with Some Account of the Drainage of Hatfield Chase (1829). p.24
Hatfield Town Council, ‘Parish History‘
For more on the discussion which Hatfield, see here.
You can find a list of the children of Richard, Duke of York, and Cecily Neville here.