JSFiddle - React, Tailwind, and code Playground
HTML
<a class="btn" id="reg1" rel="btn_region" href="#">Выбрать №3</a>
<a class="btn" id="reg2" rel="btn_back" href="#">Выбрать №1</a>
<br><br>
<input type="radio" name="radio-set" id="st1"/> №1
<input type="radio" name="radio-set" id="st2"/> №2
JavaScript
$(document).ready(function() {
$("#reg1").click(function() {
$("#st2").attr("checked", "checked");
});
$("#reg2").click(function() {
$("#st1").attr("checked", "checked");
});
});