My research has proven that I am a cousin to, not descended from, Pres. John Adams and his son.I have done a lot of research on the Adams line.You may want to look at a book that is known as the Old Adams Genealogy. I don't know where you can get a copy unless on line at Amazon and then it is very expensive.
My ancestor, Leiut. Henry Adams, b. 1620 was a brother to Joseph Adams, b. 1626.Joseph's line, third generation down, you will find Pres. John Adams.
Mary Adams, a third cousin to John Adams, and one of my great great grangmothers, married a Wilder in New York and I connect through them.