You may have noticed that some Muslims kiss the nails of their thumbs and rub them on their eyelids while hearing the Prophet's name during the Adhan. The question is whether this is permissible or not and who are the people practising such a thing?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
What some people do when they hear the name of the Prophet (Blessings and peace of Allah be upon him) being said during the Adhan like: kissing the nails of their thumbs, there is no evidence for it. Some of them believe that it protects them from blindness. This is all innovation. So, Muslims should not do these things, neither should they believe in them.

Those who do such things are not confined to a particular Madhab (school of thought) or a particular Islamic group.
Allah knows best.