A nice discovery: today I ran into a proposal in Róna-Tas’ “Turkic Influence on the Uralic Languages” (The Uralic Languages, 1988) that Mongolian qota(n) ‘fence, town’ might be an old loan from early Selkup through early Kyrghyz. Indeed, there is a Selkup word that Janhunen gives as qëtty ‘town’ and derives from Proto-Samoyedic *wåč → *wåč-əjə ‘fence’.
On the other hand, this qota(n) has been long also included in the whole ‘house, hut’ Wanderwort bundle (stretching from ocean to ocean: English hut to Ainu kotan), which includes also Uralic *kota. And there’s a consonant mismatch in Selkup that points rather in this direction! Alatalo gives (and does not connect with each other) the common Selkup forms *kuəču ‘tributary’ (#1903),  but *quəččə ‘town’ (#1912), with the velar / uvular contrast clearly attested also in the descendant dialects. Since Selkup *quə- is usually from Proto-Samoyedic *kå- rather than *wå- (e.g. *quət- ‘to kill’ < *kåə-tɜ-, but *kuətə- ‘to raise, grow’ < *wåtå-), we could trace the latter also back to a PSmy *kåt¹ɜ < PU *kota. The semantic development ‘fence’ > ‘town’ is maybe common enough, but could be here only an accidental similarity: no other Samoyedic languages seem to show this.
PU *t >> Selkup *čč  looks off, but not extraordinarily so: there are other examples of evidently secondary *č in Selkup too, most prominently PU *sënə > PSmy *t¹ën > Selkup *čën ‘sinew’. Maybe contamination from the ‘fence’ word is possible…? especially if Mongolic also shows this sense (though a quick look at Tower of Babel does not mention it).
In any case we seem to end up with the following results:
- we have cleared out one of the exceptional cases where *w- supposedly > *q- in Selkup;
- *kota ‘house’ does have a reflex even in Samoyedic;
- the Turkic and Mongolic words can be also derived already directly from Proto-Samoyedic, or even outright Proto-Uralic, without needing to wait for *w- > *k- in Selkup.
 Per -u this is surely derived though. Apocopated forms like Tym kuədž ‘dam’ probably reflect more original *kuəčə < Proto-Samoyedic *wåčə.
 It seems to be not really dateable if an irregular *t > *č shift took place in Proto-Samoyedic, in Proto-Selkup, or even in just Southern–Central Selkup.