Thought I would post this synthesis that I understand from all the threads and postings here (and a couple more I've found from Google Books)...
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Joshua Burton, senior...
(Later indications he was a Yorkshireman)
1773-1776 Births of Joshua's children in Leeds (Joseph, Joshua, Ann), mother unnamed
1785 'Joshua Burton became pastor on 25 October 1785, dismissed from Bramley in Yorkshire' [the year must to be erroneus - should be 1778] (Journey = 65 miles)
1788 'This day Mr Joshua Burton came to Sutton to exercise his Ministerial Gifts among us' 24th April
1788 'This day Mr Joshua Burton was received into the Church Fellowship.' 25 October
1790 left for Foxton, Leics (Journey = 58 miles), commencing there October
(Note SiA Birth dates are in different hand after 1790)
1792 Joshua Burton 'came near' to Kettering, Northants (journey = 15 miles)
1806 Marriage at Foxton - 16th July 1806 - by License [Joshua Burton, Wid, of the parish - (Dissenting Minister) & Mary Blackwell of St Mary le Bow, London]
1819 'List of monies received ... by Baptist Missionary Society ... 1819' 'Foxton ... by Rev. Joshua Burton 7.0.0 [L.s.d.]' (Baptist Magazine, 1819)
1821 'A funeral service was also preached for him [Rev. John Ayer, aged 81] at Braybrook by his aged and intimate friend, the Rev. Joshua Burton' (Memoir of the late Rev. John Ayer, Baptist Magazine, 1822)
1830 'Mr. Joshua Burton ... After a pastorate of forty years ... at the time of his death, which took place in 1830.' (History of the Baptist Churches in Connection with the Leicestershire Association, 1865)
So Joshua Burton, senior seems to be living c1750 [guesswork] to 1830. His only known connection with Sutton in Ashfield is for the years 1788-1790.
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Joshua Burton, junior...
1775 Birth at Bramley Leeds - 30 January 1775 (followed by Baptism 18 September 1775) to Joshua Burton, father.
1788 Arrival at Sutton in Ashfield with family.
1790? Relocation to Foxton with family? Only aged 15! Or did he stay with siblings in SiA?
1793-1799? Arrival (if not in SiA already) at Sutton in Ashfield as adult?
1799 Marriage at St Mary, Sutton in Ashfield - 24th January 1799 - by Banns [Joshua Burton & Elizabeth Hickton, both of this parish]
1799 Birth of first child, Mary, born 3 December 1799 at Sutton in Ashfield (in register)
1801 Birth of second child, Joshua, born 11 December 1801 at Sutton in Ashfield (in register)
1801-1814 Joshua Burton seems to act as Deacon to John Whitehead
1812 Birth of another child, Elizabeth, born 1812(cal) at Sutton in Ashfield (in Burke's Peerage/censuses)
1815 Succeeds John Whitehead (d 1814) as Pastor
1817 Dies at end of 1817 (at Sutton in Ashfield?)
So we can be pretty sure that Joshua Burton was living 1775 to 1817, and was Pastor in SiA for three years 1815-17.
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1) The 'birth' register for SiA seems to be a register of all children in his congregation, drawn up c1790 by Joshua. Possibly from older records, possibly orally from their parents. Later pastors seemed to add onto the last page until 1810, probably contemporaneously as these entries are in different hands.
2) The 1780 wedding seems to be a red herring - it's after the birth of JD(sen)'s children and before he seems to have arrived in Notts.
3) The line '1778 - 25th October - This day Mr Joshua Burton was received into the Church Fellowship. He died 30th December 1816 - He seems to have become a General Baptist.' can't be right on my reading. It wrongly jumps from JB(sen) to JB(jun). But is JB(jun)'s death 1816 or 1817 - where is the reference?
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So, any corrections or additions to the above?