Learn Turkish: Güya olağanüstü marifetler göstermişmiş! - He supposedly performed extraordinary feats!

This is the compound inferential form, used to express strong doubt, sarcasm, or mockery. The first -miş forms the reported past tense ('he reportedly showed'), and the second -miş acts as a past copula adding a layer of 'so he claims.' Together, they translate to 'he supposedly showed (but I do not believe it).'

If göstermişmiş already implies disbelief, isn't güya redundant?

It might seem repetitive, but it is extremely common to pair the adverb güya (supposedly / allegedly) with the -mişmiş ending. It serves as an intensifier for the speaker's sarcasm, making it crystal clear from the very beginning of the sentence that they think the claim is nonsense.

The translation says 'performed', but the Turkish verb is göstermek (to show). Is this a set phrase?

Yes. In Turkish, you 'show' a feat, skill, or trick rather than 'performing' or 'doing' it. The phrase marifet göstermek means to demonstrate one's talents or to pull off a clever trick, and it is frequently used when describing someone who is showing off.

How is the word olağanüstü constructed?

It is a compound adjective made of olağan (usual, ordinary) and üstü (above, over). Much like the English prefix 'extra-' means 'outside' or 'beyond', olağanüstü literally means 'above the usual', giving us the word 'extraordinary'.