Surname origin
 'Smith, blacksmith, farrier' William le Smyth
1275 Assize Rolls Somerset.
'Worker at the smithy' Robert atte Smyth
1332 Subsidy Roll Sussex.
A Dictionary of English Surnames by P H Reaney. OUP revised third edition 1997. 019860092-5.

Jane SMITH (c.1777 - 1832) married Charles FITT (1758 - 1843) on the 19th October 1798 at Selborne by licence, both 'of this parish'.
I have not found Jane's baptism, but she could have been the daughter of George Smith (c.1740 - 1823) and Mary GUBBY (c.1745 - 1791).
These are the children of George and Mary SMITH.
• James (1766 - 1855) = Lydia CARTER (1770 - 1857)
  • Lydia (1791 - )
  • James (1793 - ) = Elizabeth NASH
  • William (1796 - ) = Maria CANNON
  • Lucy 1798 - ) = William GALE
  • Maria (1801 - )
  • Thomas (1804 - 1829)
  • Benjamin (1806 - ) = Mary ?
  • Henry (1808 - ) = Lucy FAIRMINGER (1809 - 1854)
  • Hori (1812 - 1875) = Mary Ann LOE
• George (1768 - ) = Joyce LINTOTT
  • Susannah (1793 - )
  • Cicely (1795)X
• Sarah (1770 - )
• William (1773 - 1847) = (1) Sarah DEWYE (1782 - 1811) = (2) Elizabeth HOAR
• Martha (1775 - ) = James LEMON
• Jane (c.1777 - 1832) = Charles FITT (1758 - 1843)
  • Harriet FITT-SMITH (1796 - ) = Jeremiah SCARVILL (1790 - )
  • Charles FITT-SMITH (1797 - 1842)
  • Frances FITT(1799 - 1900)
  • Benjamin FITT (1800 - 1869) = Dinah CHRISTMAS (1827 - 1873)
  • Edward FITT (1803 - 1893) = Mary Anne McCarthy (c.1824 - )
  • Frederick Warne FITT(1804 - 1878) = Sarah DANCASTER (c.1808 - )
  • Eliza FITT (1809 - ) = Jesse RIVERS
  • Arthur James Warne (Ward) FITT (1811 - 1879)
• Ann (1779 - )
• Thomas (1781 - )
• Lucia (1783 - 1874) = (1) Richard ETHERINGTON (1776 - 1828) = (2) William DEDMAN
• John (1786 - ) = Mary DEWYE
• Kerenhappuch (1788 - ) = James JAMES
• Kezia (1790 - 1801)
• Warwick (1791)X
So why should Jane be the daughter of George and Mary Smith?
1. There is a gap between Martha and Ann for Jane's baptism c.1777
2. A Martha Lemon (née Smith) witnessed the marriage of Charles Fitt and Jane.
3. Benjamin Smith (1806 - ), the son of George & Lydia above, is described as 'kinsman' by Edward Fitt, son of Charles and Jane, after the 1830 riots in Selborne.
   Edward Fitt stated that Benjamin had worked for him 'all his life.'
   They were, in fact,  cousins.