Which part of speech is the underlined word in the following expression? 'It cannot stay at one place.'

In the phrase 'at one place', the word 'one' modifies the noun 'place' by specifying quantity/number. Words that come before nouns to specify or quantify them (such as 'one', 'two', 'a', 'the', 'this', 'some') function as determiners. Here 'one' is a numerical determiner indicating a singular specific place. It is not a pronoun (it doesn't replace a noun) nor an adverb nor a particle.