$(document).ready(function () {
    var yOff = 15;
    var xOff = -20;
    var pathToImage = "https://cdn.sstatic.net/stackoverflow/img/apple-touch-icon.png";

    $(".text-hover-image").hover(function (e) {
        $("body").append("<p id='image-when-hovering-text'><img src='" + pathToImage + "'/></p>");
        $("#image-when-hovering-text")
            .css("position", "absolute")
            .css("top", (e.pageY - yOff) + "px")
            .css("left", (e.pageX + xOff) + "px")
            .fadeIn("fast");
    },

    function () {
        $("#image-when-hovering-text").remove();
    });

    $(".text-hover-image").mousemove(function (e) {
        $("#image-when-hovering-text")
            .css("top", (e.pageY - yOff) + "px")
            .css("left", (e.pageX + xOff) + "px");
    });
});

span {
    text-decoration:underline;
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<p>This is my paragraph with a <a class="text-hover-image" href="#">very special hover</a> effect on the link.</p>
<p>Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.</p>
<p>The hovering works with every element that has <span class="text-hover-image"> a class of <em>"text-hover-image"</em></span>