I have some information, but no sources, so I don't know how accurate it is....
The parents of Anna Fiske are
Reverend John Fiske b. 20 March 1607/08 St. James, South Elmham, Suffolk, England, d 14 January 1676/77 in Chelmsford, Massachusetts and Ann Gipps(AKA Ann Gibbs)of Frenze Hall, Norfolk, England, d. 14 February 1670/71 Chelmsford, MA.Two know children: Anna and Reverend Moses b. 12 April 1642 in Wenham.
John Fiske received his degree at Peterhouse Coll., Cambridge in 1628 or 1629.He arrived in New England in 1637, lived for about three years in Salem as a preacher and tutor. He was ordained on 8 Oct 1644 in Wenham, Massachusetts,where he continued as a preacher for some 14 years. In 1656 he moved to Chelmsford, where he spent the remainder of his days. He had six children.
Notes for John FISKE:
fromSAVAGE, VOL 2 DICT. FIRST SETTLERS OF NEW ENGLAND
FISKE, JOHN, Wenham, son of that John who died 1633 (and was son of William, son of Robert, who was son of Richard of Laxfield in Queen Mary's time); born as Mather tells (in Magn. III. c. 24), about 1601, at St. James parish in South Elmham, a subdivision of the hundred of Wangford, County Suffolk bred at King's College Cambridge. There took his A. B. 1625, though Mather makes it Emanuel, married at eight and twenty years of age, by the same authority 1629, Ann Gipps of Frinshall, County Norfolk, had, as tradition said, two
children who died as infants but two others he brought with his wife and a younger brother, perhaps William, to Boston, 1637, sat down first at Cambridge, but removed the same year to Salem, freeman 2 November 1637, taught the grade school among his pupils one being famous afterward as Sir George Downing, minister for Cromwell and Charles Il at the Hague, had John, born 29 August, baptized 2 September 1638, died under nine years; Sarah, 24, baptized 26 July 1640; Moses, born at Wenham, 12 April, baptized at Salem by Mr. Norris in June 1642, Harvard College 1662; he had preached occasionally for Hugh Peters, and removed to be minister at Wenham, ordained 8 October 1644, had there Ann, 15 January, baptized 12 March 1646, being the first baptism in that church, Eliezur, 8, baptized 14 February 1647, died young; removed 1655 to and was minister of Chelmsford, where his wife Ann died 14 February 1672, "after living with him about 37 yrs." This renders Mather's account of the marriage in 1629, impossible and also the tradition of his having had four
children in England as she was his first wife and makes it probable that he brought only one child. On 1 August following, he married Elizabeth, widow of Edmund Henchman, and he died 14 January 1677. His daughter Ann married Captain John Brown of Reading, and died 30 May 1681, aged 35.
The reverend's parents were John Fiske b. Abt. 1580 at Saint James, South Elmham, Suffolk, England and d. Abt. 14 May 1633 at Saint James, South Elmham.and Anne Lawter d. 1637 at sea.married about 1601 with five children John, Martha, William, Anne and Nathaniel.Anne married Francis Chickering and d. 05 December 1649 in Dedham, Massachusetts.