Please tell me concerning the type of socks on which massah can be made.

There was cotton socks in times of the prophet. But the socks on which is sunnah to make massah is not the type of our cotton socks. Yes if you have mozas or sealzskin socks which are impermeable, strong to walk with and prevent dirt inside, then it is permissible to do massah on it. It is reported in the last Hajj, the holy prophet SAW ordered those who had mozas to cut it below ankles(sunan). As such sahabas could walk the distance of easily 25 kilometres with such socks. That is why ulamas disagree to equate our cotton socks with them. As such it is permissible to make massah on mozas and not on normal cotton socks.