Am assuming that you are using RM9, try the Gazetteer tool for looking up city names. As your screenshot states, the CountyCheck tool verifies counties, states, and countries, not cities. You should find a different result for Onondaga County.
Rootsmagic defaults to the city, county, state, country place name standard but you don’t need to follow that. Often, details like the cemetery name are added to the ‘Place Details’ field though this is also your choice.
SO what is happening is that the check is looking for a place (town) in Syracuse County, New York. You are being told that Syracuse County never existed int he state of New York, which to the best of my knowledge is true.
The underlying problem is that the whole place name system that RM supports is based on a scheme of city, county, state, country. RM did not invent this system, but it supports it. This system figures out which item is city and which item is county etc. by counting commas. It’s looking for the city of St. Agnes Cemetery in the county of Syracuse. In my view, this place name system has a vast number of weaknesses.
I think the best strategy in RM for validating place names is to turn County Check off, to use RM’s Gazetteer feature as an advisor only and not as an authority, and to use resources external to RM as your authority. Actually, I do use RM’s Gazetteer quite a bit and I’m not trying to minimize its value. But I think of it as a first draft of a place name and not a final draft.
Of course it also depends on whether you to choose to use the administrative details of a place at the time of the event (ToE) or the present day details. As we all know these are subject to change! I do not use countries that did not exist at the time of the event. Some users prefer to use the present day form for ease of geocoding but I have never had a problem geocoding any place using its ToE details. Fully agree with the advice to use external resources as the authority whether you are using ToE or present day.
For those using present day details one should of course be aware that today’s details are not cast in stone and if things change one would have to go back and revise your data as necessary to remain current. Otherwise those that have changed will be ToE and not “present day”!