Probably not a son of John and Frances. In his will, John deeded land to his "oldest son, John", which would rule out Thomas and Daniel.
According to records in Genealogy.com Thomas and Daniel were born in MA.
1703--made a freeman.
19 Mar 1707 he and his ife Martha, deeded for love, etc. to son-in-law Samuel GARDINER, of East Greenwich, half of 90 acre farm which I now live upon, and the other half at my decease,
04 Jan 1724 Will written, proved 25 Dec 1736. Executor wife Martha. To wife, all meveables to dispose of, and what she leaves, I give to my daughter, Ann GARDINER.. To wife, also, the income of real estate for life.
Inventory: 151£ 5s 11d viz: spinning wheel, carpenter tools, 4 neat cattle, horsekind, sheep, etc.