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 setup a condition on this field to check if is after or before some date. However, to avoid submissions with a different date that is not your range you may display an error message using a text field and hide the submit button. A sample condition can be as below:
Hope this information helps. Please let us know if you need any further help.