Samuel Merrill in A Merrill Memorial (MM), pages 291 and 300,  alludes to a confusion between two Daniel⁵s of Haverhill.  To Daniel b. 1720/1 Jan 13 to Nathaniel⁴ and Ruth Wallingford (John³ Nathaniel^2,1) he attributes three children (Nathaniel, Lydia and John) born in Bradford and Haverhill.  To another Daniel, b. 1729 June 1, son of John⁴  and Lydia Gage (Nathaniel³,^2,1) and first wife Abigail Carleton, he attributed four children  (Moses, Abigail, a child and Asa).  The confusion is real, for some references have both of these Daniels married to Abigail Carleton, and Samuel Merrill admits he did not know which one married Abigail.

This question is pretty well resolved by papers filed by Ruth (Wallingford) Merrill Wood Parker to the probate court in Atkinson, NH.  It seems that her son, Daniel Merrill, "a person naturally wanting of understanding" had been declared non compos mentis and that her son-in-law Daniel Poor (husband of her daughter, Anna Merrill) of Atkinson had been granted guardianship without Ruth's knowledge.  Ruth asked the Court to grant the guardianship to her son James Merrill of Atkinson instead of Daniel Poor.  Apparently she was unsuccessful for she asked the Court twice, once in 1768 after Poor had been granted guardianship, and again in 1782 after her daughter Anna had died in 1781.  She asked the court to "hear the compassionate petition of a distressed mother for an impotent son and grant that the said James be appointed guardian."  It seems pretty clear that this Daniel of Atkinson is not the one who married Abigail Carleton and that the children attributed to him really belong to the other Daniel.

So from MM and the MA vital records Daniel⁵ (John⁴ Nathaniel^3,2,1) and Abigail Carleton (m. 1749 Apr. 3 in Bradford) had:
  Nathaniel b. 1749 Aug. 25 in Bradford, MA (named for great grandfather)
  Lydia b. 1751 May 10 in Haverhill, MA (named for grandmother)
  John  b. 1752 Nov 8 in Haverhill, MA (named for grandfather)
  Dean bp. 1754 Aug. in Haverhill, MA
  Abigail b. 1756 Sept. 24 in Lunenberg, MA
  Hitte b. 1758 Sept. 15 in Lunenberg, MA
  Asa bp. 1760 Oct. 12 in ? Fitchburg, MA

 Abigail died 1764 June 3 and Daniel m. 1766 Sept. 17 Eunice Fellows and they had:
  Daniel b. 1767 May 7 in Ashburnham, MA
  Samuel b. 1768 Oct. 19 in Ashburnham, MA
  Billy b. 1770 Dec. 5 in Ashburnham, MA
  Joseph b. 1773 Mar 27 in Deerfield, MA