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JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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You can limit the submissions per date, but not to see only unread as well.
The only way to achieve something to that sort, would be to set the timeframe of your choice and then sort the submissions by unread.
To set the timeframe, you should check out the following guide: How to Partially Download Form Submissions as Excel/CSV/PDF?
Before/instead of downloading, but after setting the date parameter, you just scroll down to the grid report and click on the left most column header to sort by it - this is new / unread and read column.
That will allow you to see the new submissions first, followed by the read ones for the given timeframe.