Jonathan Marsh b.27 August 1767, Westfield Union CO New Jersey, (died 27 July 1799 in Warren, Ohio, USA) married Mary Day in 1788 in New York can be located on many family trees, however, I cannot find the marriage certificate for that date and an alternative date of 1789 occurs on one record, but there is no providence for either, there is another alternative marriage date of 1793 given in another tree, however, that date seems too old for the age of the parent to the children you listed. Mary Day died 12 October 1828 in Rahway, Union County, New Jersey, USA so she may have returned to live with family after Jonathan's death in 1799.This link is more likely.
The children of Jonathan Marsh and Mary Day
John Marsh b.21 March 1794 Alden, Erie, New York, USA. d.19 April 1855 Twelve Mile, Cass County, Indiana - possibly incorrect link as the dates and location do not exactly match the parents or grandparents and have not located a birth certificate although birth date does match the year date for birth that you provided. I pick up another John Marsh born 1794, Cincinnati, Clermont, Ohio, USA and died in Germantown, Mongomery, Ohio, this John Marsh is more likely to be correct but no exact vital dates located. He may have married a Catharine Leavell on the 28 July 1833 in Miami County, Ohio.
Child of Jonathan Marsh and Mary Day
Jacob D. Marsh, b.10 September 1798, Ohio. d.26 April 1891, Bartholomew, Indiana, USA
I pick up parents for this Jonathan Marsh, a John Marsh b.1738 Westfield, Union, New Jersey, USA (died 10 Jan 1804, Franklin, Warren, Ohio, USA) and married to a Nancy Searing on the 21 November 1762 in New York, New York, USA. She was born about 1745 (much younger than her husband) Elizabethtown, NJ, USA and she died about 1800 in Warren, Ohio, USA.
Jonathan Marsh b.1738 was the son of Jonathan Marsh b.? and Mary Jewell b.?1714 Elizabethtown, Essex, New Jersey, USA and d.9 December 1805 Westfield, Union, New Jersey, USA (This Mary Jewell seems too old for the birth date of her husband and therefore more research is required because her child bearing age would not fit well with his youth and it would be unlikely that the parents of Jonathan Marsh would have supported the marriage. Personally I think the trees online that have this connection are probably incorrect).
Although I think that the Mary Jewell is not the correct marriage to Jonathan Marsh, her parents were George Jewell (1644-1734) and Susanna Jane Pangburne (1660-1734)
Other information that may or may not be helpful, it may be completely unrelated.
July 15, 1721. Samuel Green made oath before Hez. Wyllys, Just. Pac. that saw John Marsh sign his mark, and seal the above, etc Aug. 1, 1727. Hez.Goodwin made oath to the same effect.
10:174. Jan. 8. 172 7-S.
Capt. John Marsh Lt. Nathaniell Marsh, Capt. Joseph Marsh and Jonathan Marsh, sons heires and Executioners of the Last Will and Testament of John Marsh late of Hartford deceased now exhibited an agreement under their hands and seals for a settlement of Estate to and amngst the heires, and before this Court acknowledge the same to be their free act and deed, which agreement is by this Court accepted and ordered to be recorded and kept on file [ No reference to the record of this paper is found in the Index by whoever listed this information on line]
Paper on File, dated Jan 6, 1727-S
To John Marsh, Nathaniel Marsh, Joseph Marsh and Jonathan Marsh (land described. amt. 73 00 00)
And we do further agree to pay what debts may be due from our fathers estate in equal portion. Also agreed that the remaining part of the second Meadow Lott to the value of fifty shull shillings to be equally divided between Joseph and Jonathan.
Mem. Bond. Dated Jan. 8 1727-8. A bond is filed with above paper, signed by these four brothers, being the sons of John Marsh.