What is the ruling on the repentance of one who did not record the absence of a sick student, in response to the request of two of his classmates, fearing the consequences of informing the professor?

If the sick student is not marked absent and their truthfulness is overwhelmingly presumed, then there is no blame upon you. However, if they are marked absent, then they should have been marked absent. Correcting the error is possible by informing the doctor, as long as no harm is feared.