The Spreadsheet does not allow customization of the Filter menu out-of-the-box. There is an existing feature request in our Feedback Portal about it, so I suggest casting your vote for it.
A possible workaround is to bind to the click event of the .k-icon element, and prepend the button to the .k-action-buttons div.
$(".k-action-buttons").prepend("<button class='k-button customBtn'>Custom Btn</button>");
alert("Your custom code")
Here you will find a small Dojo example for reference.
Feel free to ask if you have any questions.
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