Despite some 335 years of Byzantine control, not much survives locally from this period in terms of buildings and structures but other archaeological evidence suggests a flourishing trade present between the 6th-8th centuries AD. 
The Byzantines were seasoned traders and masters of navigation. Their merchant ships would have been a regular sight around our coast, and all across the Mediterranean.

Byzantine coins became Malta's currency after the collapse of the Western Roman Empire, and until the Arab occupation of 870 A.D.
The last such coins in local circulation would have been those of Emperor Michael III, who reigned from 802-867 A.D. and possibly those of Basil I, who reigned from 867-886 A.D.
By the end of Basil's reign, Sicily too had fallen to the Muslims, leading to the end of production of coins in the West.  
Byzantine coinage was made in a variety of mints across the Empire, but there are no records of any produced within the Maltese Islands. 

As a result, a mixture of coins having the same respective face value, but originating from different mints were hence the legal tender here. This is comparable to the euro currency of this age, with coins having the same value and overall features, but different countries of origin. 
Before going into further detail, it is necessary to give a brief overview of the monetary system in use through this period.

The currency consisted of mainly two types of coins comprising the Solidus, also known eventually as Nomisma or Bezant, originally a relatively pure gold coin, and a variety of bronze coins called Nummi. 

Byzantine currency became distinct when in 498 A.D., Emperor Anastasius reformed the late   Roman Empire coinage system. 

In the sixth century / early 7th century a manual worker would earn around 9 Folles daily.
A family’s vegetable allowance for one day cost around 5 Folles, while in times of shortages a pound of fish cost 6 Folles and a loaf of bread 3 Folles. The cheapest blanket was worth ¼ of a Solidus, a second-hand cloak 1 Solidus, and a donkey 3-4 Solidi.

The Byzantine monetary system went through various reforms over the centuries, and eventually reflected the decline of the Empire. The first major reform occurred in the 7th century when the 40 Nummi (Follis) became the only bronze coin to be regularly issued. 

Although Justinian II attempted a restoration of the Follis size of Justinian I, it continued to slowly decrease in size. Another result of this reform was the actual style of the coins, which departed from the traditional iconography by the placing of a bust of Christ on the obverse, and a portrait of the Emperor on the reverse. 

These innovations inspired Islamic Caliph Abd al-Malik, who had previously copied Byzantine styles, to develop a distinctive Islamic style, with only lettering on both sides. 

This was then used on nearly all Islamic coinage until the modern period, while European rulers eventually followed a simplified version of Byzantine patterns, with full face ruler portraits on the obverse.

Silver coins were rarely produced with the only regularly issued silver coin being the Hexagram, first issued by Heraclius in 615 until the end of the 7th century, minted in varying fineness with a weight generally between 7.5-8.5 grams. It was followed by Miliaresion established by Leo III the ceremonial Isaurian in around 720 A.D., which only became standard issue from around 830 A.D., until the late 11th century, when it was discontinued after being severely debased. By the end of the empire the currency was issued only in silver and minor copper coins with no gold issue, after the latter had come to be wafer thin!

This after various attempted reforms of the gold currency, between the 9th Century and 1347, by when Byzantine coinage gold issues were discontinued and a regular silver issue was commenced. The denomination was the Stavraton issued in 1, a half, an eighth, and a 16th of its value. Also issued were the copper Follaro and Tornesse.

After 1400, Byzantine coinage became insignificant, as Italian money became the predominant circulating currency in the West, and Islamic currency in the East and territories occupied by the Arabs / Ottomans.