Is it permissible to wipe over the khuffayn if socks are worn underneath them, or is it a condition that the khuff directly touch the skin?

It is permissible to wipe over the khuff (leather slipper) for one who performed ablution and then wore a sock, and then a khuff over it before the occurrence of hadath (impurity). It is not a condition for the wiped-over khuff to be in direct contact with the skin of the limb, and the ruling applies to the upper one. However, if one wears the khuff over the sock after the occurrence of hadath, then one should not wipe over the khuff, but rather over the sock that was worn after a complete purification.