It’s most likely you’re thinking of the early “school / backpack” style BTS photoshoot from around 2014, where Taehyung and Jungkook looked half asleep and Jungkook was kind of slumped next to V.

Fans often reference this as an “iconic Taekook sleepy photoshoot,” and clips and edits of it have circulated in Taekook fanspaces for years, so in fandom time people usually place it in BTS’s rookie era, roughly 2013–2014.

Because these are fan nicknames and memories rather than an officially titled “half-asleep Taekook photoshoot,” there isn’t a precise official date, but it traces back to that early era and has been resurfacing in posts and edits ever since.

Bottom note: Information gathered from public forums or data available on the internet and portrayed here.