The question asks us to identify the composition that was not written by Harshavadhana. Harshavadhana was a famous Indian playwright and poet who lived in the 7th century. Let`s examine each option provided:

Option 1: Harshacharita. This was indeed composed by Harshavadhana, so it is not the correct answer.

Option 2: Ratnavali. This play was also written by Harshavadhana. So, it is not the correct answer.

Option 3: Priyadarshika. This was another play written by Harshavadhana. So, it is not the correct answer.

Option 4: Nagananda. This was a play composed by King Harsha, but not by Harshavadhana. Therefore, this is the correct answer.

In conclusion, the correct answer is option 4, Nagananda, as it was not composed by Harshavadhana.