Using the w3schools example you referenced, we can simply set the src of the modal image manually:
<!-- Trigger the Modal -->
<img id="myImg" src="img_snow.jpg" alt="Snow" style="width:100%;max-width:300px">
<!-- The Modal -->
<div id="myModal" class="modal">
  <!-- The Close Button -->
  <span class="close">×</span>
  <!-- Modal Content (The Image) -->
  <img class="modal-content" src="your-image.jpg">
  <!-- Modal Caption (Image Text) -->
  <div id="caption"></div>
</div>
Then we can adjust the JavaScript so the src attribute is not overriden:
// Get the modal
var modal = document.getElementById("myModal");
// Get the image and insert it inside the modal - use its "alt" text as a caption
var img = document.getElementById("myImg");
var modalImg = document.getElementById("img01");
var captionText = document.getElementById("caption");
img.onclick = function(){
  modal.style.display = "block";
  //  modalImg.src = this.src; <- Remove this line!
  captionText.innerHTML = this.alt;
}
// Get the <span> element that closes the modal
var span = document.getElementsByClassName("close")[0];
// When the user clicks on <span> (x), close the modal
span.onclick = function() {
  modal.style.display = "none";
}