I think I need a little more clarity in the question.
If you are asking whether or not you can request from the other side to include in their affidavit a paragraph that refers to you - then the answer is no. Both sides determine what they want to address and what they want to omit from their evidence.
To clarify further, I am the respondent in a matter and the applicant has made a statement in his affidavit about me (which I believe is false). Am I able to ask the applicant for the evidence relating to that statement before the court hearing begins ?
It is up to the individual writing the affidavit to provide the evidence either as an annexure or exhibit. You can respond to the statement in the applicant's affidavit with your version or even point to the lack of evidence.
You can respond to this allegation, in your own affidavit, stating that you reject the assertion made at paragraph (whatever number) and follow with the information you believe to be true.
You haven't said which court is hearing the matter (Family Court, Federal Circuit Court, other) and the court rules determine what can and cannot be done. Procedural questions can be hard to answer without knowing the case history as the case history may also qualify the answer. A query like this is why you need a lawyer.