There is actually an article on exactly this subject by S. Kyriakidis here.

Focusing on the stories of Phokas and Skleros against Basil II, the two duels, between Phokas and Skleros, and then between Basil and Phokas, probably didn't happen, as did a lot of famous battlefield duels in Byzantine historiography.

To start off, let me paste references from Skylitzes and Pselllos, the two main sources on the duels. Each account is rather brief but too long for me to paste into a reddit comment. (Here is also a link to Psellos's first chapter which is on Basil II)

For Psellos the duel between Phokas and Skleros occurs in Chronographia 1.9-10. Psellos emphasizes that Phokas was supposedly a giant who could kill men with one stroke. In the battle, Skleros, seeing an opportunity, recklessly charges at Phokas and hits him square on the head with all his strength. However, Phokas survives, returns the blow, and leaves back for his line, embarrassing Skleros and causing his army to rout.

In Skylitzes, the duel is in chapter 16.9-10 of the Synopsis (p. 309-310 of Wortley's translation). Phokas, seeing the battle turning away from his favor, charges at Skleros, who cuts the ear off of Phokas's horse. Phokas then strikes Skleros on the head and knocks him off his horse, making Skleros's army retreat.

The duel between Basil and Phokas happens in Chronographia 1.16-17. Phokas charges straight for the young Basil. Basil, clutching an icon of the Virgin Mary, prepares to meet him when Phokas suddenly falls off his horse dead.

Skylitzes has this in Chapter 16.18 (P. 319-320 of the translation) and his account is essentially the same.

The primary speculation is that Phokas may have died of a heart attack but it's mostly acknowledged that he died before the battle with Basil, while the Phokas/Skleros simply didn't happen. So then, how do we know that these duels were probably invented? Mostly because they were just way too cinematic and aren't really supported by other sources. Firstly, both authors had, or relied on sources with, a pro-Skleros bias (See C. Holmes's Basil II and the Governance of the Empire, half of it deals with Skylitzes and the Skleros/Phokas revolts.).

Of course, Skleros loses his duel with Phokas, but this scene was a way for the two authors to soften the blow to Skleros's pride of losing the entire battle. By claiming that Skleros valiantly charged for Phokas and landing a blow on him or his horse, he is still portrayed as a courageous and noble warrior despite the reality of his failed rebellion.

Likewise, Phokas probably died before his battle with Basil. The way he died is unknown, but it likely was something anticlimactic, such as a heart attack.

So, for the most part, these fantastical battlefield duels between commanders in Byzantium were mostly a literary device, evoking scenes from the Iliad and the Old Testament.

Even then, Byzantine literature actually didn't really emphasize dueling before the 12th century. From the 6th-11th centuries CE, we have around 5 cases of Byzantine commanders entering specific, single combat situations with enemy commanders, only one of which, about the emperor Herakleios in the 7th century, occurs before the 10th century. This was primarily because Byzantine warfare invovled commanders leading from the back. Consequently, φρόνησις (phronesis, meaning wisdom) was the preferred martial trait displayed through generalship and strategy (See P Magdalino's The Empire of Manuel Komnenos, specifically chapter 6 "The Emperor and his image").

To illustrate this point, lets look at Psellos's account of the battle between Basil and Phokas. Immediately after Phokas's death, Psellos writes:

At all events, he [Phokas] fell, he who until then could neither be wounded nor taken alive, a piteous and mournful sight. As soon as the rival armies saw what had happened, the one was immediately split up and retreated, their close-packed ranks broken, their rout complete. The emperor's forces, on the other hand, immediately after Phocas's collapse, leapt upon him, scattered his Iberian body-guard, and chopped him in pieces with repeated sword-blows. His head was cut off and brought to Basil

Even after the confrontation between Basil and Phokas, Psellos returns back to what happened to the armies. A more typical example can also be in 7.70 of Psellos in the emperor Isaac Komnenos's battle against a Pecheneg incursion.

In fact, they [the Pechenegs] had not the courage to defy a man whom they looked on as ‘wielder of the thunderbolt’, and when they saw the unbroken line of Roman shields, they abandoned the idea of fighting in mass and attacked in isolated groups, howling their war-cries. But they found the romans too compact for them, and having discovered that they could neither catch them by ambush nor face them in open battle, they made a proclamation that they would fight on the third day from then.

Here the barbarian Pechenegs are disorganized and split up into groups but can't do anything against the solid Roman war lines.

Of course, I did say duels don't really occur in literature until the 12th century, and believe me when I say these duels become way more colorful than the ones in Psellos and Skylitzes. This was constituted by a noticeable shift towards the quality of andreia (ἀνδρεία, meaning something like "strength," "courage," "boldness," or "manliness") (See chapter V of War Writing in Middle Byzantine Historiography by K Sinclair for more)

The first ones I'd like to look at occur in the epic poem which became popular during the Komnenian period in the late 11th-12th centuries, Digenes Akritas about a Byzantine warlord on the frontiers of the Empire (conspicuously named Basil but usually given the title "Digenes Akritas" or "two-blooded border-lord") who goes around killing bandits and wild animals and sleeping with anybody he wants.

In one episode, Digenes elopes with his beautiful young wife who is the daughter of a general and member of the powerful, aristocratic, Doukas family. Angered by this, the Doukas general (who is never named) sends out a literal army of thousands against Digenes, which our hero promptly destroys single-handedly.

All by himself he [Digenes] dared encounter thousands, And in a short time slaughtered countless soldiers, All fully armed and mounted, trained for war. He first advised them to turn back again, And not to undertake to test his valor, But they, ashamed to have one man defeat them, Preferred to die instead of being shamed. He started forward, drawing out his sword-club, And, ere the General came, not one was left. (P. 50 of the Hull translation)

To emphasize my point, Digenes is not commanding a group of soldiers against this army, he is personally killing every soldier against him. And Digenes's personal prowess is a major theme he strangles lions and bears at the age of 12, has a duel with an Amazonian, and even kills a drakon (δράκων, could be a dragon or a serpent). This is essentially Byzantine hyper-masculinity at its finest.

Admittedly, this is the fantasy literature of the Byzantine world. Did anything like this happen in historiography? The answer is: to some degree.

As an example, I would point to John Kinnamos's 12th century account of the reigns of John II and Manuel Komnenos (Using the Brand translation, titled Deeds of John and Manuel Comnenus). It focuses mostly on Manuel's reign and is quite unashamedly praising of him. In one vague scene, Kinnamos writes of Manuel in a battle against the Turks:

Many of the Romans were then valiant, but the emperor most of all. When the enemy pressed closest, very strongly, he rushed with his spear and broke their shield-wall, not merely individuals, but many in pairs. (Page 78 of the translation)

Again, Manuel is not merely commanding his armies against the Turks, but he is personally creating decisive victories through his own physical prowess. Even more cartoonishly, Manuel is depicted as also going out into the wilds and killing random beasts. In one scene, Manuel personally encounters a vague beast described as leopard-like in appearance but with the size of a lion and naturally, kills it (p. 200). Kinnamos mentions immediately before this how random bouts with animals was simply a common occurrence for Manuel.

These are two extreme cases of andreia in Byzantine literature, but the rise of such attitudes led to a new focus on heroism and personal action in battle, of which the duel was one aspect. We can see even later cases of this such as Theodore I killing a Seljuk Sultan in battle in Akroplites's 13th century history (Akropolites even has one account of a trial by combat) or Andronikos III challenging a Bulgarian tsar to single combat in Kantakouzenos's 14th century writings.