@benteh This is more of a Yinglish (Yiddish-English) word than a #Yiddish word. It shows up in "The Joys of Yiddish" but not any of my usual resources or dictionaries. The website you cite in another post doesn't exist. When I see a lot of English language resources on a Yiddish word, that usually gives me pause, as it's unlikely any of the sources actually speak Yiddish.
As for origins, "patshken" is to smear, paint poorly, or dirty. This is a Slavic root, also present in Russian as пачкать and Polish as paćkać (ala wiktionary: https://en.m.wiktionary.org/wiki/%D7%A4%D6%BC%D7%90%D6%B7%D7%98%D7%A9%D7%A7%D7%A2%D7%9F )
"Far" is an "inseparable verbal prefix serving to: a) create or emphasize transitive verbs; b) express removal, disappearance; c) express degradation, a negative effect." Hence the participle "farpatshket", written with an o in an American English accent. (See also oyspatshken and onpatshken with similar meanings.) That's all just transliteration, of course... it's written פֿאַרפּאַטשקעט in Yiddish.