Ingred,
без onclick ...
<!DOCTYPE HTML>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
.check{
background-color: Red;
}
</style>
</head>
<body>
<script src="https://code.jquery.com/jquery-3.3.1.min.js"></script>
<a id="cat_3" href="#" class="opacity_filter checkshadow3 isExcept" >
<img src="put/put2/put3/vase.svg" class="a_check my-1 graycategory" title="Категория 3" height="48">
</a>
<script>
$(function() {
$(".checkshadow3").click(function(event) {
event.preventDefault();
var img = $(this).toggleClass("check").find("img")[0];
img.src = img.src.replace(/(_a)?\./, function(a, b) {
return b ? "." : "_a."
})
})
});
</script>
</body>
</html>