Is it permissible to pray after removing the shoes, subsequent to wiping over them, while keeping on the socks that were put on in a state of purity?

The prayer you performed after taking off the shoes you wiped over—there is a difference of opinion among jurists regarding its validity. The view that it is valid is narrated from some Companions, such as Ali (may Allah be pleased with him), who performed ablution and wiped over his sandals, then took them off and prayed. However, it is more prudent to repeat it as a precautionary measure to avoid the difference of opinion.