An anyathāsiddha cause is, in Nyāya, a cause wrongly established. The Nyāyakośa (sub voce) explains that it is a kind of cause where one mistakes something previously existent for the cause. As an example, Annambhaṭṭa's Tarkasaṅgraha mentions the ass which has carried the clay and the final pot (ghaṭa). Therefore, to say that the pot exists because of the ass would be a case of anyathāsiddha. It is true that the ass existed before the pot, but it is not true that it is its cause (which should be essential to the result).
The Nyāyakośa mentions, among others, the instance of the stick (daṇḍa) and the pot. Is anyone aware of the usage of sticks while producing clay pots? Perhaps as part of the potter's wheel?