/u/itsallfolklore has previously answered What are the origins of the pointy witch and wizard hats?

/u/TheLionHearted has previously answered When did the classic wizard hat first appear in fiction and does it have any historical precedent?

Other redditors may have more to say on the topic.

That Duns Scotus bit is interesting. But conical caps predate him by a long shot.

The Phyrigan cap (freedom cap), a brimless conical cap was worn by Phyrigans of antiquity and remains in use by various Balkan peoples. This was confused with the stiffer pilos given to freed slaves in Rome, so became associated with freedom, hence Phyrigan cap was a symbol of freedom in the days of American Revolution and the French Revolution. This cap (unlike the pilos) is soft and the tip falls over, so this is the same hat visually associated with gnomes (garden variety or otherwise), and 20th century Smurfs (cartoon), rather than the stiff thinking cap Duns Scotus endorsed.
There is a late 6th century mosiac portraying the 3 Magi (wise men from the East) bringing gifts to the infant Christ at Basilica of Sant' Apollinare Nuovo in Ravenna, Italy. The magi are wearing floppy phyrigan caps. An even earlier mosiac, from the 5th century at Santa Maria Maggiore shows the Three Magi also wearing similar caps.

The Pilos (hat) was a short, stiffer, brimless conical hat often worn by Illyrians and ancient Greeks. (Latin: pileus.)

The "witches” of Subeshi, a set of mummies dated to 4th-2nd centuries BCE and located in the Tarim basin-- specifically in a high gorge east of Turfan (or Turpan, in Xianjing, People's Republic of China), wear very tall, pointed black hats that resemble the iconic headgear of their sisters in later medieval Europe.
The Scythians were frequently portayed in art as wearing backswept conical hats and indeed they became linked to pointed caps as well. They also wore elaborate helmets with pattens, always conical in some fashion.

An even earlier conical hat type was the golden hats of bronze age Central Europe, possibly worn by precursors to the Scythians-- short and some very long and elaborate. Of the latter, only 4 examples are known. These are long elaborate conical hats made out of sheet gold, with tiered stamped patterns, often disc and circle motifs. All but one (the golden hat of Schifferstadt, the first one found, in 1835) have star motifs embossed at the apex.
The Avangon Hat was found in 1844 in a field outside Poitiers, France, brim missing, so it is more conical than the other examples, and it has been dated to 1000-800 BC.

Non-hat related, but intriguing in this context: The Nebra sky disk is the oldest known representation of the cosmos-- it is bronze with a blue-green patina and inlaid with gold symbols-- sun or moon, lunar crescent, and stars. It is dated possibly to 1600 BCE. It was found at a site near Nebra, Saxony-Anhalt, Germany by two unlicensed treasure-hunters in 1999.

So I'd say these are the earliest examples you could find. Stiff conical caps have been used in various contexts, usually with brims, sometimes without (such as the masked Capirote used by the Spanish Inquistion) pretty continuously.

Medieval noblewomen wore the hennin in the 15th century (1430 onwards), hence our "princess hat" This was much mocked by lesser classes as extravagance. Our modern party hat seems to trace from the caupuchon (still used in Cajun Mardi Gras) from late mediveal France. But per John Beusterein, mediveal codes often dictated conical hats as punishment. As it died out elsewhere, the Spanish Inquistion rekindled it in Spain as a tool of public shame.

John Beusterein's "The Celebratory Conical Hat in La Celestina,” Crime and Punishment in Medieval and Early Modern Europe, ed. Connie Scarborough, Berlin and New York: de Gruyter, 2012. 405–415 is an interesting source on medieval codes and conical hats as punishment if you want to learn more. These hats were not the same as the masked capirote. They’d leave the face exposed, like a unshrouded hennin or a party hat. Sometimes the hats were painted with words of their shame (like scarlet letters.)

Regardless, I am pretty sure Duns Scotus didn't invent the conical cap, anyway!
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Let's go back to Scythians just because they're kinda cool and they are the "people in pointy hats" in Greek art. They ruled the Pontic steppes for a while and had contact with China, Europe, being integral in the Silk Road. They were the among the first to master mounted warfare, and established one of the first nomadic empires. As such they were ascendant as an independent tribe around 800 BCE until 300 AD when they were assimilated by other tribes. They became ascendant over the Medes around 650-630 BCE and extended their powers to the borders of Egypt. They vanished from history after the Hun invasions of 5th century AD. We know them mostly from Greek writing and Herodotus (our most important source for their religion/gods), their art and artifacts, kurgan burials, and stone carvings showing them wearing conical caps.

Their art incorporates animals, including mythological beasts like birds, hoofed animals, griffins, solar and cosmic symbolism, and started changing around 500 BCE when they experienced considerable Greek contact and eventually became Hellenized. Per Herodotus and other sources, their kings were considered holy and of solar and heavenly origin. Their religion is considered pre-Zoroaster in type, with cannabis to invoke trances and divination done by soothsayers. They frequently had kurgan-type mounds.

We have no extensive writings by them. They were not a literate people, and fragments in Greek and Persian are the most we have to go on, but they seem to have spoken an East Iranian language; many words known seem closely related to Ossetian, which is regarded as probably a direct descendent of Scythian. The Issyk inscription found in a Kurgan is thought maybe to be Scythian, but it remains undeciphered. The upshot is that the Scythians had a pretty black, barbariac reputations from the Ancient Greeks onwards, but also were known to have fabulous wealth from trade and raids.

In the Middle Ages, "Scythians" became a catch-all term for various nomadic barbarians (many quite unrelated to the original Scythians, such as Huns, Goths, etc.), thanks to Greek sources emphasizing the barbarity of the Scythians.

Shakespeare even alluded to legend that Scythians ate their children in King Lear. Byzantine sources called the Rus raiders "Tauroscythians" even though they were not ethnically related. The connection between Scythians and barbarism was so deep English writers such as Edmund Spenser and Willian Camden writing on Ireland, sought to find relationships between the Irish and the Scythians to prove their barbarous nature.

Interestingly, many peoples (Poles, etc.) claim Scythian descent, and the Irish are no different-- the Irish-language book 11th century (Lebor Gabála Érenn The Book of Invasions) identifies he origins of the Irish and the Scots in an ancient prince of Scythia called Feinius Farsaid who was a master of all the languages.

Ancient Roman sources such as Julius Caesar, though failed to draw connections between the two people in such disparate places. Although he wrote something about druids, he did not describe them in appearance nor note any head gear.

The only Celtic head-dress found-- from the "the Deal Warrior" burial around 200-180 BC, that could have been possibly druidic is a thin headband with a cross-strap over the head-- too thin and shallow to be part of a helmet, but perhaps a base for a cloth or bark hat, although there is no such remnant found as far as I know.

It is possible the reputation of the Scythians caused the conical caps to be used as a mark of unchristian/barbarous/shameful behavior in the Middle Ages, but I don't see any literature establishing this connection. Why in this context the hennin would have suddenly achieved vogue is unknown to me. I would suspect cultural transmission from the Crusades, perhaps, but again, I do not know.