akshaykotha
If there is an option
over whether, will it be right?
akshaykotha , although you did not ask about the word "debate" used as a verb or a noun, the distinction is important.
If (1)
debate were a verb as it is in this case; and
(2) there were two choices,
debate whether and
debate over whether; then
(3) we would choose
debate whether.
As a verb,
debate means
to argue about. We do not need another preposition such as "over."
DEBATE AS A VERB
Correct: Members of the teachers' union
debated the contract.

Correct: Members of the teachers' union
debated whether to accept the contract.

Incorrect: Members of the teachers' union
debated over whether to accept the contract.

The last sentence is equivalent to saying:
Members of the teachers' union
argued about over whether to accept the contract.
IMPORTANT: If debate is a NOUN, "debate over whether" and "debate over" are both correct
DEBATE AS A NOUN
HERE is a recent official question in which debate is a noun and "debate over" is used.
I have seen a few idiom collections in which "debate over" is listed. I suspect that these lists may be the source of your question.
Please note
(1) that "debate" in the "idiom list" case is a noun
(2) that when answering the official question I cited, you do not need to decide whether "debate over" is better than "debate on." Other and more definite errors can be used to eliminate answers.
One source, HERE, does not think that the official question tests the "debate over" idiom.
Takeaway: If debate is a verb, do not use OVER.
If debate is a noun, "debate over" is common and acceptable.
I hope that helps.