Children
1-John Case b. 28 Jul 1616 [Gravesend England] Aylesham, England m. Sarah Spencer abt 1657 at Simsbury, Hartford, CT. 1st spouse was Elizabeth Moore.
2-Thomas Case died w/o children
3-William Case died on Martha's Vineyard in 1634.
4-Richard Case who came over at a later time. Richard settled in Hartford CT where married and later died in 1694. He left a son and 2 daughters.

Gen 2
John Case (b. 1616) was the only one of these to pass on the name. He married Sarah Spencer in 1657 in Hartford CT and they had 10 children: John, Elizabeth, Mary, William, Samuel, Joseph, Richard, Sarah, Abigale and Bartholomew. 

***John and Sarah (Spencer) Case were married in Windsor CT in 1657 and moved to a 'suburb' which later became Simsbury. The letter states that Simsbury by 1800 had so many Case's living there that it could be called 'Case-town'. About this time many moved to the West (I know the most about the ones going to Ohio.) 

Gen 3
William Case born 1665 in Windsor, Hartford, CT, died 31 Mar 1700. His father was John Case born 25 Jul 1616 Aylesham, England, his mother was Sarah Spencer 20 Apr 1636, Hartford, Co. CT. William married Elizabeth Holcomb in 1688, in Hartford CT. I don't know if this is your William Case but it's a good bet. John Case came to America with 3 brothers, I believe one was a William Case also. There father died enroute to America. I have further genealogy of Sarah Spencer, also brothers & sisters of William. John Case was the first Case to settle in the New England area. On my line the Case family moved from CT to NY then to Ill. But I know some moved to SC.