Is it permissible to wipe over socks if I feel a liquid discharge after performing ablution but before fully putting on the socks, given that there is an excuse that makes ablution difficult?

It is a condition for the permissibility of wiping over the khuff (leather socks) that they be worn after a complete state of purity, based on the saying of the Prophet, peace and blessings be upon him: "Leave them, for I put them on while I was pure." So, if you are certain that a fluid exited before you finished putting on the socks, your purity is invalidated, and wiping is not permissible. Rather, you must wash your feet and put them on again while in a state of purity. However, if the exit of the fluid is merely a doubt or a whisper (waswasa), do not pay attention to it, and wiping is permissible for you.