It may generally depend of the rules applicable in the concerned court, however, usually such affidavit is required.
I have seen that in the Supreme Court, Delhi High Court and even in CAT, the application for condonation of delay is required to be supported by an affidavit of the party concerned.
In the Supreme Court, generally a composite affidavit is prepared which covers the SLP and other Criminal Misc. Applications (including one for condonation of delay) in the same affidavit. But, in Delhi High Court, usually a different affidavit is required for the application for condonation of delay.
You may have to check the rules applicable for the particular court (where you want to file such application) on this issue. But, generally, an affidavit may be needed for this purpose.
Dr. Ashok Dhamija is a New Delhi based Supreme Court Advocate and author of law books. Read more about him by clicking here. List of his Forum Replies. List of his other articles. List of his Quora Answers. List of his YouTube Videos.