Hello Browny,
Nothing definite, but here goes:
Census night, Sunday, Apr. &th, 1861, Ref: RG9/4521, folio 91,
a John NESBITT, unmarried, age 29, Ordinary Seaman, is aboarda ship "Hylton" at Holyhead, Anglesey.
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1851 Census: 51 North Street, North Shields. Ref: HO107/2409, Folio 313, p.10:
Margaret NESBITT, Head, Widow, age 56, Housekeeper, born Hull, Yorkshire
John NESBITT, son, 18, Boat Builders Apprentice, b. North Shields.
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1841 Census: North Street, North Shields. Ref: HO107/825/10 fo 7. p 7:
John NESBITT, 43, Teacher
Margaret NESBITT, 45
Elizabeth NESBITT, 13
John NESBITT,8.
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It looks like you will need to get John's marriage certificate to verify his father's name and occupation before you could claim these as yours.
Good luck.
Trini.