The iron-on patches being worn by some of Taiwan's air force pilots are a defiant message to Xi, who is often satirised for looking like the honey-loving cartoon bear.

"It's amazing. It's the happiest thing in recent days," social media user Mark Sasha Liang said on Facebook.

Chen Kai-chu, another fan, said: "Wear this to go through Chinese customs."

China, which claims the island as part of its territory, launched three days of massive war games on Saturday that involved simulating attacks on democratic Taiwan.

The show of force from Beijing was a response to Taiwan President Tsai Ing-wen's meeting with US House Speaker Kevin McCarthy last week.

Taiwan's defence ministry released a series of images and videos during the drills to show off its military preparedness.

One picture in particular, of an airforce pilot inspecting a fighter jet, immediately caught the eye of social media users.

They noticed on the sleeve of his jacket a patch featuring an illustration of a flag-wielding Formosan black bear pounding Winnie the Pooh.

The discovery set off a social media storm.

Two of the badges have the word "scramble" at the bottom, one of them also proclaiming "we are open 24/7".

A third badge designed last year shows a Taiwanese fighter pilot slapping a panda, China's national symbol.

It was produced when China carried out similar exercises in response to then-US House speaker Nancy Pelosi's visit to Taipei last year.

Taiwanese people have rushed to buy the Pooh-punching patches, which sell for 200 Taiwan dollars (US$6.50).

The badges originated at Wings Fan Goods in Taoyuan city, east of the capital Taipei, where they have now sold out.

"It's so famous that my friends on the other side of the Pacific are asking me about this," fan Mob Liu said on Facebook.

A Facebook vendor who sells the patches said he has received around 1,000 orders since the image went viral on Saturday.

Most of the requests are from Taiwan but order requests have also been received from China and Hong Kong.

"The people of Taiwan are disgusted with China's overacting military exercises after the Tsai-McCarthy meeting so this pilot's badge sparked discussion," said the Facebook vendor, who asked to be identified by his business name Wizardgeo.

"The people support the military in defending our sovereignty."