Abstract The study aims to examine the syntactic and semantic behaviors of predicative possession (i.e., have-possessive constructions) in Malwai Punjabi, an underdocumented dialect within the Indo-Aryan language family. Data were collected from longitudinal online interviews with native speakers as consultants, with audio recordings for transcribed target sentences. The results revealed that all the alienable possession, either permanent/temporary or abstract/concrete, could be marked by the postposition koḷ ‘near/with’, whereas inalienable possession, such as whole-part relation and kinship, could not be encoded using koḷ. The prototypicality model and schema-based metaphors explained why koḷ was widely used to express alienable possession in Malwai Punjabi. The analysis of companion and proximity schemata also justified the extended semantics of predicative possession, suggesting a metaphorical mapping of accompaniment and location onto possession. From a typological angle, the case study can not only provide further evidence for the existence of split possession but also contribute to a cognitive understanding of predicative possession in relation to other languages.