Hello I had a quick look at the Cavan Facebook genealogy pages and think I see your query there, At the remove you are at it is really necessary to have a religion to see if any church records survive, it they were Church of Ireland (Protestant) the surviving records are listed here https://www.ireland.anglican.org/cmsfiles/pdf/AboutUs/library/registers/ParishRegisters/PARISHREGISTERS.pdf About 40% to 50% were lost in our civil war in 1922. I think is is possible they may have been Presbyterian and then records are more difficult, Methodist I understand are not online etc
I can find no record of Gott name but on the off chance I looked at the Down Survey (means the land was measured by laying down chains hence Down) nothing to do with County Down. I see there are 2 Hassart people listed as owning land nearby in 1670, just slightly north of Ture in County Fermanagh, this would indicate to me and I am no expert on the precise history that the people listed were important people in Cromwells army, senior officers who received land in the Plantation of Ulster see here http://downsurvey.tcd.ie/landowners.php th)ere are also two Hassart people in the Flax Growers List of 1796 in Fermanagh (this is Northern Ireland) https://www.failteromhat.com/flax/fermanagh.php I see two Hazard people in County Down on this list.
It is not simple to find the link to your possible people and the Fermanagh people but my view would be they are the same family, however if you want to research these families you would need a professional genealogist and there is a list on the National Library website, I understand from a course I was on that if you can link to the 1700s early that is you can often get further back and as this appears to be a plantation settlement there may be more records. https://www.nli.ie/en/homepage.aspx
I looked in the Registry of Deeds Index Project here https://irishdeedsindex.net/index.php there is a Gott or two Gott families in Omagh, County Tyrone in 1739 and 1740 and I see a Robert Hassard with a lot of property in Dublin and he appears to live in Mount Hassard, County Fermanagh. They appear to be families of worth so I recommend you try cotacting the local libraries in these areas and also have a look at the PRONI website, Public Records Office of Northern Ireland, all these places are close to Cavan where you are looking except Dublin but the main residence appears to be Fremanagh, also you could check and see if there are wills of any of these people. But my main recommendation to check all this is to seek a professional who should scope out the work for you and give you a price in advance. Also you have to accept the spelling changes in the names but that is a common enough thing to change.
Good Luck,
Pat
