Praise be to Allah.
Firstly:
It is permissible to wipe over socks, if they are thick and cover the ankles.
As for thin socks, it is not permissible to wipe over them according to the majority of scholars, and it was narrated that there is consensus regarding that.
Ibn Qattan (may Allah have mercy on him) said: All are agreed that if the socks are not thick, it is not permissible to wipe over them."(Al-Iqna‘ fi Masa’il al-Ijma‘ 1/90).
Similarly, it is not permissible to wipe over socks that do not cover the ankles, according to the majority of jurists.
Please see the answers to questions no. 228222 and 176866 .
Secondly:
There are medical socks which exfoliate the skin to remove dead skin cells and soften the skin. They are called exfoliating socks, and they are of different types.
If they are thick and cover the ankles, it is permissible to wipe over them if they were put on when one was in a state of purity.
But if they are thin and show the colour of the skin, or they are thick but water goes through them, and it is not usually possible to walk in them, then it is not valid to wipe over them.
If someone needs to wear them and does not want to take them off every time they do wudu, then he can wear thick socks over them and wipe over the outer socks.
Please see the answer to question no. 259422 .
And Allah knows best.
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