How can prayers that were performed with clothing that was later discovered to have impure semen on it be made up, and should they be made up consecutively or at the times of their corresponding prayers?

The preponderant opinion is that semen is pure. And whoever prays in a garment that has impurity on it, being unaware of it, his prayer is valid and he is not required to repeat it. However, whoever prays while in a state of major ritual impurity (janabah (definition)), either forgetting or being unaware, and then realizes it, is required to repeat the prayer according to the majority of scholars. He must make up the prayers immediately and in their proper order.