How to restore deleted submissions?

Unfortunately, once you deleted the submission data manually, it is not possible to restore them.

What you can do is, collect the submission data from the notification email and create an excel file using the data then you can use Import App to import the excel file to your Submission page.

Import-App-Easily-Import-Your-Excel-or-CSV-Data-into-JotForm

You follow the guide to check the email logs: How-to-View-All-Your-Form-Email-History