A new family of geometric Borel measures on the unit sphere is introduced, which extends the L 0 p-capacitary measures proposed by Zou and Xiong (J Differ Geom 116:555–596, 2020). In this paper, we consider the existence of the solution to the p-capacitary dual Minkowski problem when 1 < p < n and q < 0 . Moreover, log-Minkowski style inequality for dual mixed p-capacity when q < 0 is established