All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
In principle, the socks should cover the ankles because it is an obligation to wash them [ankles] when washing the feet when performing ablution, and this is a condition for the validity of wiping over them when performing ablution.
However, the obligation for the socks to be under the ankles applies only to the person who is in a state of Ihraam for Hajj or ‘Umrah if he is not able to find slippers other than these socks, in which case he should cut the socks in a way that they should be under the ankles. It might be that this is what you mean about the meaning of the narration which is reported by Al-Bukhari which reads: ‘‘Ibn ‘Umar said: “A man asked the Prophet saying: “What should a person in the state of Ihraam wear?” The Prophet replied: “He should not wear a Qamees (long shirt), or trousers, or a hooded cloak (burnoose) or a cloth touched with saffron nor Waras (a kind of dye that has a smell), and whoever does not find slippers, he should wear socks but he should cut them in a way that they will be under the ankles.”
Allaah Knows best.