I really liked the added wrinkle in Blade Runner 2049 where replicants have to periodically prove that they're sufficiently robotic.

Also, "Impostor", still by P.K.Dick

https://en.wikipedia.org/wiki/Impostor_(short_story)

More like https://en.wikipedia.org/wiki/Evidence_(short_story)

More like Second Variety

https://en.wikipedia.org/wiki/Second_Variety