People familiar with online Finnish slang will know that the word paska ‘shit’ has been developing morphological variants. Most prominently, for several years now, it has had a variant partitive singular paskea besides the usual paskaa. A YouTube video uploaded on Xmas 2014 is often credited for popularizing this. Attestations occur much earlier though. At least two blog posts from 2008 and 2012 are still found already by Google, several further attestations turn up in the Suomi24 Corpus 2001–2017 (starting from 2007) and one also in the Ylilauta Corpus 2012–2014.
In origin this form is probably not completely arbitrary. paska does double duty in colloquial Finnish as a noun: koiran paska ‘dogshit’; and as an adjective: paska koira ‘a shit(ty) dog’. (The second sense is probably a calque from English.) Also, -ea is a common adjectival ending, no longer actively productive but still available to analogical extension at least. So my hypothesis would be that paskea was first coined as a nonce adjective ‘shitty’ or ‘shit-like’. Good reference points for analogy would be e.g. ruskea ‘brown’, surkea ‘terrible’. Early on, Suomi24 uses tend to be indeed mostly adjectival: äärimmäisen paskea käyttökelvotonjärjestelmä ‘extremely shitty inoperating system’, se paskea väri ‘the shit-like color’, verisen paskea vaikutelma ‘bloody-and-shitty impression’, linsucks on (…) paskea mm. musiikin tekemisessä ‘linsucks is shitty e.g. for making music’ (from 2013–2014).
As the next step, a predicative construction N on paskea (593 Ghits), equivalent to N on paska ‘N is shitty’, could be with a little linguistic creativity also parsed as a partitive mass noun construction, equivalent to N on paskaa ‘N is shit’. From here it’s possible to branch into what seem to be the most common other usages: interjective constructions like hyi vittu paskea ‘ew fuck [that’s] shit’ (313 Ghits; appears in the YouTube source and probably often quoted from it), mitä paskea ‘what the shit’ (229 Ghits), ihan paskea ‘really shit’ (127 Ghits); or oblique case constructions like translative paskeksi (71 Ghits), essive paskena (38 Ghits), ablative paskelta (21 Ghits), adessive paskella (16 Ghits). Subject or attribute uses like paske juttu ‘[a] shitty tale/event’ (9 Ghits), pasket housussa ‘with shit in pants’ (6 Ghits), paske haisee ‘smells of shit’ (1 Ghit) remain less common. I can actually also find attestations of nominative singular in -i (e.g. paski juttu 6 Ghits), showing that it’s not even clear what inflection type a partitive paskea would imply.
More common by an order of magnitude is however a contraction noun paske : paskee- (pasketta 7140 Gh, paskeeksi 723 Gh, paskeella 290 Gh, paskeessa 261 Gh…); attested from Suomi24 at least since 2004 and heavily also from Ylilauta. This, however, has in much of its uses a more specific meaning ‘shitty product’: car, computer hardware or software, music, etc. This would appear to be an independent derivative/coinage, and also one following normal Finnish word derivation patterns, not any kind of weird analogical development.
Starting from this, reanalysis of the nominative paske could even also yield the unalternating e-stem discussed above… but this is not supported by the heavily oblique-stem uses of paske-, nor by the different semantics. This however does not have to mean that the recent development of these two word groups would be unrelated entirely. Since adjectives in -ea are rendered as -ee in colloquial Finnish (kovalevy on paskee ‘[the] hard drive is shitty’), the other option is that the adjective is what has been inspired by this derived noun, then still followed by analogy to an e-stem noun as outlined above. Partitives, too, take part in this smoothing, so also the original analogy from an adjective to a partitive could have happened before standardization from paskee to paskea.
If this all checks out, the history altogether is then as follows:
paska → paske : paskeen ‘shitty product’ (by 2004)
reanalyzed → paskee ‘shit.PART’ (by 2007)
standardized → paskea (by 2008)
extended → paske (? paski) : pasken ‘shit’
Stage 2 actually finds its first attestation only by 2012; but all attestations available to me are scarce before 2014. No doubt all of these have moreover spent their early years in more ephemeral media like chatrooms before appearing into reliably archived writing.