The sentence provided is: "Each of the students have submitted their assignments on time."
The correct form of the verb should be used to ensure subject-verb agreement. The subject of the sentence, "Each of the students," is singular because "each" refers to each individual student. Therefore, the verb should also be conjugated in the singular form.
The underlined portion "have submitted" should be corrected to "has submitted" to maintain proper subject-verb agreement. Thus, the corrected sentence becomes:
Each of the students has submitted their assignments on time.