Dear Dr. Dayakrishn Purohit

In p type semiconductors the sign of the carriers (using an experiment measuring the Hall effect) is positive, i.e., they are holes. About metals I do not, but metals have an intriguing property: "if the valence is almost filled then, the quasiparticles that are moving at the top of the band are holes", so those could be in principle the ones that the Hall effect measures.

Also there is the so called "Adiabatic positive Hall effect" if the charge carriers are only holes, then the temperature gradient and the electric potential gradient are directed in the same direction.

I guess you can check the quite extensive literature on the Hall Effect and find about those statements I tell you.

Kind Regards.