The year 1000 anxiety?

The canon was largely fixed by the third century, so by the end of the tenth the influence of the apocryphal gospels is limited. It's likely to be Revelation 20:

And I saw an angel coming down out of heaven, having the key to the Abyss and holding in his hand a great chain. He seized the dragon, that ancient serpent, who is the devil, or Satan, and bound him for a thousand years.
... When the thousand years are over, Satan will be released from his prison and will go out to deceive the nations in the four corners of the earth — Gog and Magog — and to gather them for battle. In number they are like the sand on the seashore. They marched across the breadth of the earth and surrounded the camp of God's people, the city he loves. But fire came down from heaven and devoured them.
... Then I saw a great white throne and him who was seated on it. The earth and the heavens fled from his presence, and there was no place for them. And I saw the dead, great and small, standing before the throne, and books were opened. Another book was opened, which is the book of life. The dead were judged according to what they had done as recorded in the books. The sea gave up the dead that were in it, and death and Hades gave up the dead that were in them, and each person was judged according to what they had done. Then death and Hades were thrown into the lake of fire. The lake of fire is the second death. Anyone whose name was not found written in the book of life was thrown into the lake of fire.

— NIV

There is at least one cavil to be raised: if Satan had been bound, it would be more likely to have been at the Resurrection (say, year 33) so the thousand years would end around 1033.

But the description of the end of the world and the General Judgement could certainly have engendered apocalyptic fear towards the end of the first millennium.

Jewish tradition had a belief that the length of normal history would be six thousand years, followed by a thousand year time of peace, corresponding to the day of rest in Genesis 1. Many early Christians had the same idea. However, due to problems with numbers for the ages of people in the Septuagint, the early church had a wildly inaccurate date for the creation. Thus they thought that the seventh millennium would commence ca 500-600 AD, at which time the church faced millennial fears. In AD 723, the Venerable Bede reasoned that the creation was in 3952 BC based on his own Chronological research, a more recent date by many centuries. This would push the start of the sixth millennium to 1048 AD or thereabouts. Venerable Bede also popularized Dionysius Exiguus' new dating system, years anno domini. Thus people now had a popular way to date events since Jesus' birth and a revised estimate for when the next millennium would begin. Combine that with the idea of a thousand year reign of Christ from Revelation and you had a recipe for fervent expectation - and later disappointment.

See https://answersresearchjournal.org/comments-usshers-date-of-creation/

In virtually every century A.D. there have been events that caused people to think "the end of the world" was nigh. Some of them might have been aware of prophetic literature speaking of the matter, whether or not that came from Christian sources, pagan ones, or what you refer to as 'apocryphal gospels'. Even before a full one thousand years had passed from Jesus' foretelling a time of trouble unprecedented in all world history (Luke 21:25-27 & Matthew 21:21-22), world events became catastrophic.

The year AD 550 was so shockingly appalling that Christians the world over were convinced "the end" was nigh. There was 12 to 18 months of thick, persistent dust clouds that darkened all the skies between Europe and Asia Minor. It blocked sunlight and caused the temperature to drop, causing crop failure. Cloud stretched as far east as China, where frosts and snow were recorded in the summer months. Tree ring data over Europe, Siberia, Mongolia, Argentina and Chile, reflect decreased tree growth that lasted more than a decade. Due to crop failures, famine and drought, upwards of seven out of ten people were killed in northern China and Scandinavia due to famine or disease.

Furthermore, the dust cloud coincided with the Justinian plague which may have been exacerbated by the weakened immunity of the malnourished remaining population.

“A failure of bread in the year 536 A.D." - The Annals of Ulster [Ireland]”.

“A failure of bread from the years 536-539 AD.” - The Annals of Inisfallen

“During this year [536], a most dread portent took place. For the sun gave forth its light without brightness... and it seemed exceedingly like the sun in eclipse, for the beams it shed were not clear.” - Byzantine historian Procopius' record in a 536 AD report on the wars with the Vandals.

“The sun became dark and its darkness lasted for one and a half years... Each day it shone for about four hours and still this light was only a feeble shadow... the fruits did not ripen and the wine tasted like sour grapes.” - Michael the Syrian

About 500 years previously Jesus may not have specifically mentioned massive dust clouds being part of that terrifying period of time, but I don't know of any apocryphal 'gospel' literature that did. However, Jesus was careful not to give any clues about dates, and it is dates you ask about. One thing is significant - any literature claiming to give a date for "the end of the world" would be apocryphal, because Jesus and the entire gospel literature in the New Testament warn against that. "No man knows the day of the hour", Jesus stated in Matthew 24:36.

The quotes I have provided were all written after the events, recording what happened over a period of time, that caused millions to fear that "the end" was upon them. That has been the case many times thereafter. And the Bible (especially in Revelation) warns of a build-up of plagues poured on the Earth, culminating in the seven last plagues just before the Last Day. (Revelation 15:1 & all of chapter 16.) No matter how bad things were in the 500s A.D., they would become far worse just before Christ's spectacular and unexpected return to usher in the Last Day. Yet still there is no clue given in God's word as to any year. Beware anyone claiming to have knowledge of, or to have 'worked out' any year for "the end"! The time for the biblical apocalypse is known only to God - Revelation 14:15-20.