Pan fried or deep fried? How do we count fatty meats that render heavily and fry themselves over dry heat?

Good question! I suspect that people had been making various fried foods for thousands of years -- as long as there's been cooking fat and a metal or ceramic vessel to retain the heat and fluids.

More source-ably (is that a word?), there are the roman globus, which was a kind of fritter described by Cato in his De Agri Cultura in the 2nd century BC. The globos is described as being made of cheese and spelt dough, and cooked in lard in a hot copper vessel. Here's a translation:

Recipe for globi: Mix the cheese and spelt in the same way [described above], sufficient to make the number desired. Pour lard into a hot copper vessel, and fry one or two at a time, turning them frequently with two rods, and remove when done. Spread with honey, sprinkle with poppy-seed, and serve.

So I have here a primary source with a recipe for a sort of sweet fried-dough-and-cheese pastry from around 2,200 years ago.

For modern style dishes like fried fish and fried chicken, that is dishes where a meat is breaded and fried, the oldest extant sources I could track down were only from about 400 years ago.

I'm having a hard time tracking down a reliable primary source, but The Good Housewife's Jewel, published in 1596, has the following description of an an English fried chicken dish (spelling, layout, and punctuation as in original):

To frie Chickins.
Take your chickins and let them boyle
in verye good sweete broath a prittye
while, and take the chickens out, and quar-
ter them out in peeces, and then put them
into a frying pan with sweete butter, and
let them stewe in the pan, but you must not
let them be browne with frying, and then
put out the butter out of the pan, and then
take a little sweete broath, and as much
Vergice, and the yolkes of two Egges,
and beate them together, and put in a little
Nutmegges, synamon and Ginger, and
Pepper into the sauce, and then put them
all into the pan to the chickens, and stirre
them together in the pan, and put them in-
to a dish, and serue them vp.

It's not clear from this description if the chicken is breaded as we would understand it today, but otherwise this is a fair rendition of a pan-fried chicken.