Whether "Byzantine" coins are "ancient" or "medieval" has been discussed many times. Ancient-coin dealers carry Byzantine coins and the few "medieval" coin dealers carry Byzantine coins. They are both.
At the beginning of the reign of Anastasius (491-518) coin denominations were as they had been under the previous emperors, a tiny copper "nummis" AE4 (those tiny monogram pieces) and gold, with essentially nothing in between. In 498 Anastasius reformed the denomination system by adding in larger "M" pieces which were supposed to be worth 40 (M = 40, in Greek) of the nummia. The first reform began with the "small module" M pieces. But, they were much less than 40 times the weight of the nummia and met with resistance. Then a second reform coin was introduced, larger, still with an M. These are the ones most commonly seen. The larger M type is accompanied by corresponding "K" 20-nummia pieces and even 10-nummia (with "I" for 10 in Greek) and 5-nummia pieces (with "E" for 5).
The smaller "M" type also has some "K" and "I" coins to go with it. They are rare.
My old (86) friend DC, who was a minor dealer asked me to sell his remaining Byzantine coins and he had some of those tiny AE4 monograms which I have not put on the site yet and two of the small-module M pieces on the page I am using:
http://augustusmath.hypermart.net/Crosses.html#ByzByzantine coins can be interesting for the numerous unlisted varieties that can be found. One on that page has a dot (globe) above the head which is not usual. The other is listed, but has an odd-shaped six-pointed star unlike most Byzantine six-pointed stars. If you like Byzantine coins, those sorts of details become interesting. You can't expect to love Byzantine coins for artistry or high grade.