Capt. Anthony Fulgham - Pedigree for Capt Anthony Fulgham of Isle of Wight, Virginia

Looks pretty extensive...

What about this as well? https://familysearch.org/ark:/61903/2:1:MWZP-KZD

it lists a Hercules as Capt. Anthony's father and Anne Hardwick as his mother. This page has some extensive info which also lists Hercules - http://www.medievalgenealogy.org.uk/families/foljambe/foljambe.shtml

Oh boy that's the proposed parents i couldn't find anything on before:

Parents seen as & Sarah Foljambe & Gen. Hercules Foljambe without attribution. Disconnected Nov 2015.

The http://www.medievalgenealogy.org.uk/families/foljambe/foljambe.shtml has this comment under Hercules:

HERCULES FOLJAMBE, 2nd son, born ....., a general and sea captain under the Earl of Cumberland, in his expedition to the West Indies, married, 1st, Sarah, daughter of John Hardwick, of Hardwick, Esq.; 2ndly, Anne .....,; 3rdly, Sarah, daughter of Edward Rye, of Aston, Esq., and widow of George Poge, of Misterton, co. Notts., by whom she had had issue, Darcy Poge and 4 other children, and died 27 November, 1632, s.p., bur. at Rotherham.

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Died s.p., Latin for "sine prole," "without issue" -- that is, no known surviving children.