I am a member of "The General Society Of Mayflower Descendants.
My ancestor, Captain Samuel Fosdick married Mercy Picket, the great grand daughter of William Brewster, Mayflower passenger.
The captain would not be a descendant, but his son Samuel II IS a descendant. The "Society" sells a book, "Mayflower Families in Progress" that you can use through the first five generations as "proof.
From there you can look through two books: "Annals of the Fosdick Family", by Raymond B. Fosdick and "Fosdick Family, The Oyster Bay Branch" by Lewis L. Fosdick. These books took me down to my gr gr grandfather.
From that point on, I used birth, death and marriage as well as an old Bible family page, pictures of tombstones and cemetery signs and census immages that I obtained from Ancestry.com. I also used obituaries.
I hope this has helped. If you need help with the books on Fosdick, let me know .