Middle names were uncommon in this era so I have removed the middle name "Maurice" although a number of My Heritage trees have this middle name. But that may be because they have copied it from Geni.
He may be the son of Esther Winchester, first wife of John Burwell of Co. Herts and Milford. But Families of Early Milford Connecticut, page 163 has the following children for John, the son of John Burwell, and also notes that he died in 1665.
John
Mary bapt 5 Dec 1653 per Milford Vital Records [comment: which makes her father the son of Esther Winchester]
Samuel born ca 1661