Is it possible to have a form that will not allow you to fill up twice from the same device?

Is it possible to have a form that will not allow you to fill up twice from the same device.

or that remembers you have fill up the form and doesn't lets you fill it up again?

Yes, this is possible using any of the settings below inside the Form builder:

1. Unique submission https://www.jotform.com/help/64-how-to-set-unique-submissions-on-a-form
2. Unique question https://www.jotform.com/help/223-how-to-set-form-limits-based-on-a-unique-question

Do review these and let us know if they help.