Total War Attila. It runs only on next gen GPUs. It looks the same as Rome 2 but slightly better. Every extra GTX Titan you add will bump up the average framerate by 1.

There are plenty ofgames covering the Roman Republic, it's expansion, its fight against Carthage, it's fall in the hands of "imperators" and the early Empire. But what the OP searches is the late Empire, thats is the Tetrachs, the Era of Constantine and sons, the christian Empire, the fall of the West, the morphing of the East into the Byzantine empire, the rise of the Frankish kingdom, the early arab invasions, Charlemagne's empire and its division.

There is very little on that. Probably because the industry tends to focuss on names and concepts that sells. Caius Julius Caesar, Hannibal ring a bell to most. The Flavian amphiteather or the Circus Maximus are also world famous. But who knows of Caesar Julianus leading its troops at Argentoratum in 357 AD? Or who would be tempted by a graphical adventure trying to solve murders in the Court of Contantius II ? Or by a political game re-enacting the time of the Tetrachs ( would look and feel like Crisis in the Kremlin in AD 285-305 ) ? Or by a game on trade in the Black Sea Region in the 8th Century ? That's how you end with Attila and the Vikings as main contributors to gaming coverage of that period.

It's wrong that this description makes me want to play that game... XD

I can recommend King of Dragon Pass, although it doesn't have any overly invasive fantasy elements (there is some religious / spirtual stuff that you may or may not class as fantasy) it is however disconnected from any particular real world history so if that's what you're looking for it may not be the game for you.

Crusader Kings isn't THAT difficult to get into.. a little more complicated then Civilisations but once you've grasped the basic concepts it's not too hard.

It fails heavily on the no Fantasy but I think Rune would fall into the right time period at least (plus from what I remember it's a lot of fun)

It might be a little earlier then the period you're looking for but what about Celtic Kings?

Hm yes you are right.
Not too much outside Europe either, I guess? How about Tibet in the 5th century? :) When they still had proper army and a strong king... I guess there is no reason these games couldn't exist. But I am one who cannot recall much outside the realm of "mainstream history" having games released. Worth looking into though, maybe there are some hidden gems.

hm. How about Lord of the Rising Sun? That's 12th century though, maybe too far into the future.
https://www.mobygames.com/game/lords-of-the-rising-sun

Fate of the Dragon comes a wee bit early compared to your 300 AD target, but it may interest you.

It's a tiny bit earlier then you asked for (100 - 250 AD) and set in China (not sure whether you were looking for mainly European stuff or not) but anything based on Romance of the Three Kingdoms would probably fit the bill. There's a host of different games (mostly made by Tecmo Koei) ranging from button mashing hack and slashers like Dynasty Warriors to grand strategy stuff (I believe those ones are just called Romance of the Three Kingdoms). I think there was a total war kind of game set in the same period but I can't remember what it was called.

Edit: I see the previous posters suggestion is actually one such game set during that period XD

I assume there are are Chinese and Japanese games . The Chinese games I know of relate to the time of Sun Tzu (500BC), to the Han Period (200 ) or to the time of the bandit kingdoms (1000AD). But There are others that have never been translated I guess. The Japanese games I know of focus on the Sengoku period (16th century) or on the Mongol expansion. I'm not aware of any meaningful game on mesoamerica that would deal with the pre-Aztec cultures (Imagine the first person adventure one could build around the high period of the Mayan kingdom-cities , 500-900 AD, that could be downright creepy and bloody and still be accurate. But I guess the public would ask laser guns and chainsaws because skinning your adversaries with polished stone and eating their heart is only fun for a while ) . No idea about India either, or Africa.

Edit : the games i refer to that are the closest to the period in question are Romance of the 3 kingdoms (200AD) , Bandit Kings of China (1000AD)

Crusader Kings II has already been mentionned, but I've just noticed this mod, which delves further into that period.