Hello John, I search Roots Ireland for any McKee born from 1810 to 1835 and found none, however I searched the Tithe Applottments and there is a John McKee in the parish of Innishmagrath, townland given in 1834, there are other McKee people but but only one John.
Here is a list of the C of I records that survive and lost https://www.ireland.anglican.org/cmsfiles/pdf/AboutUs/library/registers/ParishRegisters/PARISHREGISTERS.pdf
There is often a letter of recommendation when they jon the police but there is an excellent Facebook page, apply to join Royal Irish Constabulary A Forgotten Irish Police Force 1816 to 1922 the Royal was added in 1867 I think, one of the contruibutors is Jim Herlihy who wrote the book on the history of the RIC. They answer a lot of queries.
There are also a couple of Leitrim pages on FB one Leitirm History and Genealogy and Genealogy and a couple on Mohill on old photos if interested but I searched them for any McKee reference and no joy.
I would recommend you look at the Leitrim Library website and local history section and you can search old newspapers, get a tiny piece of the article but can request the page, about €1 I think, the library may be on lockdown but the email should be working. A number of books have been produced locally in the last 10 or so years also.
If you cannot find anything let me know, I answer queries on this site relating to Louth but my mothers family are from Leitrim, just in case there are a few ares of Ireland, called Leitirm but only one county, here is a site of townlands and civil parishes so you can see what townlands are referred to. https://www.townlands.ie/