Puede hacerlo usando el método getState en la instancia persianDatepicker , así:
var pd = $('#example').persianDatepicker({ autoClose: true, // other options }); function showUnix() { const state = pd.getState(); alert(state.selected.unixDate); } <script src="//cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.js"></script> <script src="https://babakhani.github.io/PersianWebToolkit/doc/lib/persian-date/dist/persian-date.js"></script> <script src="https://babakhani.github.io/PersianWebToolkit/doc/lib/persian-datepicker/dist/js/persian-datepicker.js"></script> <link href="https://unpkg.com/persian-datepicker@latest/dist/css/persian-datepicker.min.css" rel="stylesheet" /> <input type="text" id="example" class="initial-value-type-example inline-example leapyear-algorithmic"> <button onclick="showUnix()">show unix</button>