Колокол (Kolokol meaning “bell”) was a mid-19th century dissident Russian-language newspaper, printed in London and Geneva to evade Russian state censorship. Commenting on the lines of verse quoted by Kolya:
Long will you remember
The house at the Chain bridge
Victor Terras writes:
These two lines are from a widely known antigovernment satire, repeatedly printed in various émigré periodals and almanacs, first in The North Star 6 (1861): 214. Though it did not appear in The Bell, best known of these publications, The Bell did print a sequel to this poem (no. 221 [1 June 1866], p. 1812). […] At any rate, Dostoevsky commits another anachronism, since Kolya’s father had died many years before the appearance of any of these publications. The Bell was published from 1857 to 1867, which means that it began to appear after Mr. Krasotkin’s death.
Victor Terras (1981). A Karamazov Companion, p. 352. University of Wisconsin Press.
Here’s the first appearance of the poem (“ПОСЛАНІЯ” meaning “Letters”) in Полярная звезда (The North Star):
The two lines Kolya quotes are the last two lines of the second verse:
Будешь помнить зданіе
У Цепнаго моста.
The point of the paragraph is that Kolya is showing off, pretending to knowledge of dissident literature that he doesn’t possess: his father only had the one issue of The Bell and Kolya hasn’t even read the whole of that.