What should I do if I performed wudo while wearing socks and later on that day I put on shoes? Do I have to remove my shoes to conduct wudo or is enough to just wipe over the shoes?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

If you wear socks while being in a state of purity [after having performed ablution], and then you wear shoes, then it is permissible for you to wipe over the shoes as long as you do not take them off. If you take them [shoes] off, then it is not valid to wipe over them, and you may wipe over the socks provided the conditions of wiping over the socks are met. The evidence for this is that Al-Mugheerah ibn Shu’bah narrated that the Prophet performed ablution and wiped over the socks and shoes. [Abu Daawood]

Allah Knows best.