Green’s Dictionary of Slang

snottery adj.

also snottery-nosed
[snotty adj.]

1. dirty, paltry, contemptible.

[Scot]Dundee Courier 5 Jan. 4/2: The prisoner and two companions [...] were walking home when they were met by a constable, who [...] ill-used the prisoner, called him a ‘snottery pup’.
[US]Boston Globe (MA) 12 Mar. 6-B/1: ‘You should see the iwating room there [i.e. a prison] with the poor women with their snottery kids’.
[Ire]P. McCabe Butcher Boy (1993) 2: Some snottery-nosed young gawk.

2. unpleasant, arrogantly annoyed; thus n. snobbery.

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