HTML Code

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="utf-8">
  <title>trigger mouseenter</title>
  <style>
    body { font-family: sans-serif; padding: 16px; }
    #outer { padding: 10px 16px; background: #10b981; color: #fff; display: inline-block; margin-right: 8px; border-radius: 6px; }
    #fire { padding: 10px 16px; background: #6366f1; color: #fff; border: none; border-radius: 6px; cursor: pointer; }
    #log { margin-top: 12px; color: #047857; font-weight: bold; }
  </style>
</head>
<body>
  <div id="outer">Outer</div>
  <button type="button" id="fire">Trigger mouseenter</button>
  <div id="log">Enter Outer or click the button.</div>
  <script src="https://code.jquery.com/jquery-3.7.1.min.js"></script>
  <script>
    var count = 0;
    $("#outer").mouseenter(function() {
      count++;
      $("#log").text("Outer handler fired (count: " + count + ")");
    });
    $("#fire").click(function() {
      $("#outer").mouseenter();
    });
  </script>
</body>
</html>

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jQuery .mouseenter() — trigger no-arg (Try It)