I say, and with God's success: Al-Jurmouq: it is a small shoe worn over the khuff (leather sock) to protect it from mud and impurity, and its leg is shorter than the khuff, but it covers the ankles. The various shoes worn today are considered to be like the jurmouq if certain conditions are met. Based on this: it is permissible to wipe over the jurmouq if certain conditions are met, and the permissibility of wiping over them is supported by the hadiths about wiping over the khuffs, along with the hadith of Bilal : "I saw the Messenger of Allah  wiping over the mūq (plural of jurmouq) and the khimar (headscarf)," in Sahih Ibn Khuzaymah 1: 95, Musannaf Ibn Abi Shaybah 1: 162, Musnad Al-Shashi 2: 360, Al-Mu'jam Al-Awsat 1: 240, Musnad Ahmad 5: 264, Musnad Al-Ruyani 2: 14, Musnad Al-Shamiyin 2: 291, Al-Mu'jam Al-Kabir 1: 350, and the mūq is the jurmouq. Refer to: Al-Tayyin 1: 52, and Allah knows best.