Must one repeat the prayers that were performed after the emission of semen during sleep, while ignorant at the time that it was semen, and only realizing this after a year has passed?

If you knew that what came out of you was semen, and you did not perform ghusl for it, and you prayed the prayers while junub, then you must make them up because they were not valid. The words of Sheikh al-Islam regarding one who omits a condition out of ignorance do not apply to you, because you did not omit ghusl out of ignorance of its obligation. Rather, you thought you were not junub, and then the opposite became clear to you. And whoever thought he was ritually pure and prayed, then the opposite became clear, must repeat the prayer. Sheikh al-Islam Ibn Taymiyyah said: "And whoever forgot the purification from hadath, and prayed forgetfully: he must repeat the prayer with purification, without dispute."