The Adams genealogy is from Connecticut, and different than the one I have from New York, of which I've discussed quite a bit. In addition, I have another Adams line from Massachusetts. My direct lines are in green. If you have this surname and wish to share information, please write, and I will share my sources.
Descendants of EDWARD ADAMS
Generation No. 1
1.  EDWARD ADAMS was born 1619 in England  and of New Haven  and Fairfield , and died November 11, 1671 in Fairfield , Fairfield Co., Connecticut New Haven  / Milford ,  Connecticut Fairfield , Fairfield Co., Connecticut 
Children of EDWARD ADAMS and MARY PATCHEN were:
                   i.    MARY ADAMS, b. Abt. 1647; d. Abt. April 1712; m. (1) LUKE GUIRE, February 23, 1662/63, Fairfield, Fairfield Co., Connecticut; m. (2) MR. MERWIN, Bef. 1680, Milford, New Haven Co., Connecticut; m. (3) STEPHEN SHERWOOD, Bet. 1697 - 1701, Fairfield, Fairfield Co., Connecticut 
2.               ii.    SAMUEL ADAMS, b. Abt. 1650; d. Abt. February 10, 1693/94.
3.              iii.    ABRAHAM ADAMS, b. September 09, 1650, Fairfield, Fairfield Co., Connecticut 
                 iv.    NATHANIEL ADAMS, b. Bef. 1656; d. Bef. 1693.
4.               v.    NATHAN ADAMS, b. Aft. 1656, Fairfield, Fairfield Co., Connecticut ; d. February 06, 1747/48, Fairfield, Fairfield Co., Connecticut 
                 vi.    JOHN ADAMS, b. Aft. 1656; d. 1693.
Generation No. 2
2.  SAMUEL ADAMS (EDWARD) was born Abt. 1650, and died Abt. February 10, 1693/94.  He married MARY MEEKER July 15 in Fairfield , Fairfield Co., Connecticut 
Children of SAMUEL ADAMS and MARY MEEKER were:
                   i.    SAMUEL ADAMS, b. January 01, 1676/77, Fairfield, Fairfield Co., Connecticut 
                  ii.    DANIEL ADAMS, b. May 17, 1679, Fairfield, Fairfield Co., Connecticut 
                 iii.    SARAH ADAMS, b. October 03, 1680, Fairfield, Fairfield Co., Connecticut; d. February 24, 1707/08, Woodbury, Litchfield Co., Connecticut; m. ISAAC CASTLE.
                 iv.    ABIGAIL ADAMS, b. March 25, 1682, Fairfield, Fairfield Co., Connecticut 
                  v.    ELIZABETH ADAMS, b. February 03, 1683/84, Fairfield, Fairfield Co., Connecticut Stratford 
                 vi.    ABRAHAM ADAMS, b. January 01, 1684/85; d. 1718; m. SARAH (__).
                vii.    JONATHAN ADAMS, b. October 31, 1686, Fairfield, Fairfield Co., Connecticut 
               viii.    DAVID ADAMS, b. June 24, 1689, Fairfield, Fairfield Co., Connecticut 
                 ix.    BENJAMIN ADAMS, b. December 28, 1690, Fairfield, Fairfield Co., Connecticut 
                  x.    JOHN ADAMS, b. September 06, 1692, Fairfield, Fairfield Co., Connecticut; d. 1727, Greenwich, Fairfield Co., Connecticut; m. ELIZABETH HUSTED, 1717; d. Bef. 1730.
3.  ABRAHAM ADAMS (EDWARD) was born September 09, 1650 in Fairfield , Fairfield Co., Connecticut 
Children of ABRAHAM ADAMS and MARTHA HOBBY were:
                   i.    MARY ADAMS , m. JOSEPH MARSHALL.
                  ii.    ABIGAIL ADAMS, m. JOHN WHITLOCK.
                 iii.    ELIZABETH ADAMS, m. BENJAMIN GILBERT.
                 iv.    SUSANNA ADAMS, b. Abt. 1688; d. February 07, 1749/50; m. JOHN WINSTON, Abt. 1711.
                  v.    DEBORAH ADAMS, b. Abt. December 09, 1694; m. JAMES BENNETT.
                 vi.    HANNAH ADAMS, b. Abt. January 20, 1694/95; m. DANIEL MOREHOUSE.
4.  NATHAN ADAMS (EDWARD) was born Aft. 1656 in Fairfield , Fairfield Co., Connecticut , and died February 06, 1747/48 in Fairfield , Fairfield Co., Connecticut Fairfield , Fairfield Co., Connecticut Connecticut 
Children of NATHAN ADAMS and MARY JAMES were:
5.                i.    GANDA ADAMS, b. Bef. December 23, 1694, Fairfield, Fairfield Co., Connecticut 
                  ii.    NATHAN ADAMS, b. Bef. December 23, 1694, Fairfield, Fairfield Co., Connecticut; d. 1724; m. REBECCA CLAPHAM.
                 iii.    NATHANIEL ADAMS, b. Bef. December 23, 1694, Fairfield, Fairfield Co., Connecticut 
                 iv.    SARAH ADAMS, b. Abt. 1695; d. February 04, 1775; m. BENJAMIN STURGIS, February 09, 1714/15, Fairfield, Fairfield Co., Connecticut.
                  v.    RUTH ADAMS, b. Bef. October 11, 1696, Fairfield, Fairfield Co., Connecticut; d. June 13, 1775, Fairfield, Fairfield Co., Connecticut; m. NATHANIEL WILSON.
                 vi.    MARY ADAMS, b. Bef. October 02, 1698, Fairfield, Fairfield Co., Connecticut; d. 1767, Fairfield, Fairfield Co., Connecticut; m. LUKE GUIRE.
                vii.    JOHANNA ADAMS, b. Bef. September 01, 1700, Fairfield, Fairfield Co., Connecticut 
               viii.    AVIS ADAMS, b. Bef. November 29, 1702, Fairfield, Fairfield Co., Connecticut; m. DANIEL CROFOOT, Fairfield, Fairfield Co., Connecticut; b. of Reading, Connecticut.
                 ix.    NATHANIEL ADAMS, b. Bef. October 01, 1704, Fairfield, Fairfield Co., Connecticut 
6.               x.    STEPHEN ADAMS, b. Abt. 1708, Fairfield, Fairfield Co., Connecticut 
Generation No. 3
5. GANDA ADAMS (NATHAN, EDWARD) was born Bef. December 23, 1694 in Fairfield , Fairfield Co., Connecticut Fairfield , Fairfield Co., Connecticut Fairfield , Fairfield Co., Connecticut Redding , Fairfield Co., Connecticut 
Children of GANDA ADAMS and MOSES KNAP were:
                   i.    HANNAH KNAP, b. Fairfield, Fairfield Co., Connecticut 
                  ii.    RUTH KNAP, b. Fairfield, Fairfield Co., Connecticut 
                 iii.    DAVID KNAP, b. Abt. March 15, 1711/12, Fairfield, Fairfield Co., Connecticut; d. May 07, 1795, Redding, Fairfield Co., Connecticut; m. ANNA (__) Wife of ISAAC MEEKER, October 24, 1736, Fairfield, Fairfield Co., Connecticut; b. Abt. May 17, 1713, Fairfield, Fairfield Co., Connecticut; d. August 04, 1797.
                 iv.    SARAH KNAP, b. Abt. August 24, 1712, Fairfield, Fairfield Co., Connecticut; m. GERRARD FINNEY; b. of Dutchess Co., New York.
                  v.    JONATHAN KNAP, b. Abt. May 1715, Fairfield, Fairfield Co., Connecticut 
                 vi.    REBECCA KNAP, b. September 08, 1717, Fairfield, Fairfield Co., Connecticut; m. SIMON DEWOLF / DOLPH, 1739, Redding, Fairfield Co., Connecticut; b. March 08, 1708/09, Middletown, Middlesex Co., Connecticut; d. 1771, Northeast, Dutchess Co., New York.
                vii.    MOSES KNAP, b. Abt. June 28, 1719.
               viii.    RACHEL KNAP, b. June 07, 1726, Fairfield, Fairfield Co., Connecticut ; m. JOSIAH WHITLOCK, Fairfield, Fairfield Co., Connecticut 
                 ix.    EUNICE KNAP, b. 1728, Fairfield, Fairfield Co., Connecticut; m. JABEZ WILLIAMS, 1753, Fairfield, Fairfield Co., Connecticut.
                  x.    MARY KNAP, b. Abt. 1730, Fairfield, Fairfield Co., Connecticut; d. December 09, 1756, Fairfield, Fairfield Co., Connecticut; m. GERSHOM FAIRCHILD, November 19, 1754, Fairfield, Fairfield Co., Connecticut; b. Abt. 1734, Fairfield, Fairfield Co., Connecticut; d. December 20, 1792, Fairfield, Fairfield Co., Connecticut.
6.  STEPHEN ADAMS (NATHAN, EDWARD) was born Abt. 1708 in Fairfield , Fairfield Co., Connecticut Fairfield , Fairfield Co., Connecticut 
Children of STEPHEN ADAMS and SARAH FINCH were:
                   i.    MARY ADAMS, b. October 18, 1728, Fairfield, Fairfield Co., Connecticut 
                  ii.    JOHN ADAMS, b. April 09, 1732, Fairfield, Fairfield Co., Connecticut ; d. March 11, 1732/33, Fairfield, Fairfield Co., Connecticut 
                 iii.    SARAH ADAMS, b. September 15, 1733, Fairfield, Fairfield Co., Connecticut 
                 iv.    NATHAN ADAMS, b. October 26, 1736, Fairfield, Fairfield Co., Connecticut 
                  v.    ANN ADAMS, b. August 10, 1742, Fairfield, Fairfield Co., Connecticut 
                 vi.    ELIZABETH ADAMS, b. October 09, 1744, Fairfield, Fairfield Co., Connecticut