JSFiddle - React, Tailwind, and code Playground
HTML
<button id="botao" data-order="day-0">Clique</button>
JavaScript
$('#botao').on('click', function () {
var valor = $(this).data('order').split('-')[1];
valor++;
$(this).data('order', 'day-' + valor);
console.log( $(this).data('order') );
console.log( $(this).attr('data-order') );
});