John Baggett - Yes, Sir Hervey Bagot had a son John. Some major tweaking is needed, please.

Sir Hervey's son John was born 29 Mar 1613 in Staffordshire, England. He died in 1614.

References- which I am adding here, as the remainder of this profile needs preservation and moved to a different set of parents (i.e., the John Baggett who married Martha Mathew or Matthew, was the son of William and Sarah Bagott)

1) The Heraldic Visitations of Staffordshire made by Richard St George 1635 Page 27 (including the following footnote: "JohnBagot. Born 29 March 1613. Ob. inf. Filius et hares, atat. dim. anni 1614."
2) Collins, Arthur, Brydges, Sir Egerton, Rivington, F C, et al. Collins's Peerage of England, Volume 7, 1812, pps. 527-8, accessed 6 Jan 2019: "(Sir Hervey) By the first (Catherine Adderley of Weddington) [he] had five sons. 1. John, who died young."
3) Entry for Bagot, Sir Hervey (1591-1660), 1st bt., online blog: Landed families of Britain and Ireland, accessed 6 Jan 2019.

URLs for the above-two citations:
1) https://babel.hathitrust.org/cgi/pt/search?q1=john%20bagot;id=uva.x...
2) https://books.google.com.au/books?id=gx0wAAAAYAAJ&lpg=PA527&amp...
3) http://landedfamilies.blogspot.com/2017/12/312-bagot-of-blithfield-...

Note also for the John, son of Sir Hervey: WikiTree ID Bagot-261 https://www.wikitree.com/wiki/Bagot-261 has the correct data.
And, for the presently available, verified details on the John Baggett who married Martha Matthew, Baggett-797 https://www.wikitree.com/wiki/Baggett-797 has the correct data and family constellation.