The correct option is D suffering from jaundice
Option A: These words 'student of your school' are not relevant to the given sentence, because it's not very necessary to include that the writer is a student. By now, the identity has already been established. Also, the line that follows "The doctor has advised ...rest to help me recover fully from the sickness." sounds very vague as the nature of the sickness is not mentioned. Hence A is incorrect.
Option B: The words 'on leave' also don't refer to the "sickness". As a result, the sentence sounds vague, the reason behind the leave must be mentioned in the line. Also, the application intends to ask for a leave from the principal. It is not written to inform the principal that the student 'Ramesh' is already on leave. (This kills the purpose of the letter.) Hence B is incorrect.
Option C: Similar to option A, the name of the writer is not necessary to be included, as the format already requires the name to be written after the conclusion of the letter. Hence C is incorrect.
Option D: The phrase "suffering from jaundice" is the most appropriate option because it is relevant to the statement that follows "The doctor has advised...". It tells the receiver the reason behind which the doctor has advised the writer to rest. Hence D is the correct option.