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In the manga, the main character was left behind in his original world and his whole class was transported to a fantasy world because the main character was asleep and was out of range from the magic circle.
And so he does favors for this cop and the cop pays him with food like limited edition ramen.
This is the aptly titled My Entire Class Was Summoned to Another World except for Me (Class ga Isekai Shoukan sareta Naka Ore dake Nokotta n desu ga, 2017).
From MangaRock:
A god of a different world had abruptly appeared in Kamiya Yato's classroom and forcibly summoned the entire class to his world... except for him—because he was sleeping in a seat in the corner of the class, the round summoning magic circle didn't reach him—and he ended up staying here on Earth, but with brand-new skills.
After he made it through a whole year full of police interviews and journalism reports, he finally became a high school student, but the quiet days he had hoped for were far from over—be it terrorists who decide to occupy his school or even monsters from different world, one by one new incidents take place in the town he lives in...
Will a boy without any motivation be able to save the world?
These two pages match your recollection.
Found with the Google query isekai manga "his class" transported another world "sleeping".
