Scale mail is real, it has been around since Babylonian times. Used to be known as "Jazeraint" in the 'Orient'. In most cases the scales would be attatched to a backing of cloth, probably most often linnen or even silk. (One thing to keep in mind about leather in antiquity is that it was relatively expensive. It's also hot and not too flexible.)
This is a relief of some early sumerian warriors who appear to be wearing scale armor
Scale over mail is a much less common combination, but the Romans actually did have a version like this, I believe it was Lorica Plumata /bird feather scale (their other more conventional type variant being Lorica Squamata aka fish scale ) I might have the names backward though. The scales in this Roman armor were very small and each scale was actually bent 90 degrees and wired into a backing of mail. Most of the armor of this type has been found had scales of brass, bronze, orachulum and /or even silver, so there is considerable argument as to whether this was usually essentially parade armor (meant for display) or really meant for protection. I'm of the minority opinion that it was a real battlefield armor since it was worn by officers, the other type or Roman scale armor being worn by Auxiliary troops and Cavalry.
Plumata worn by a German re-enactor
Plumata being reconstructed by an armorer
A modern re-enactor in Lorica Squamata
Ancient (bronze?) scale armor recovered by archeologists, believed to be roman
(Dacian?) Squamata depicted in Roman relief
Anyway, generally speaking mail is much more effective as armor than scale. In Medieval Europe mail basically replaced scale almost completely by the end of the Dark Ages.
It was however much more common to see lamellar armor, (something kind of like scale armor but with larger scales aka lamelae wired or lashed to each other in rows) worn over mail. That was common in the East particularly, from Russia to Arabia, from Classical times into the Renaissance.
This is some lamellar armor from Wisby
This is a depiction of "Klibanion" armor of the Byzantines which is Lamellar over mail.
I think Ringmail is basically a fantasy invented in the 19th century and perpetuated by D&D but I have seen a Russian variant on bakharets ("half armor" or reinforced leather) which used rings over leather. A rare type and not at all common in Western Europe certainly.
"Studded leather" is another major fallacy incidentally, 99% of the time it's misidentified brigantine...
Jeanry