What is the ruling on the prayer of one who prayed while unaware of the presence of impurity on his hand (remains of feces under the fingernail), knowing that his fingernails were short and he had washed his hands with soap before ablution, and is he required to repeat the prayer after discovering the impurity?

It is not obligatory to repeat the prayer for someone who prayed in ritually impure clothes, being unaware of the impurity therein, and his prayer is valid. Some scholars recommend repeating the prayer within its prescribed time for someone in your situation, but there is no sin upon one who omits what is recommended, so there is nothing upon you. It is obligatory to beware of obsessive whisperings.