Clear input value on dynamically add/remove inputs

Use .on as shown below. The elements that are being added afterwards are not getting binded with the functions that you need.

Updated function

$(document).on("input", "input", function() {
  $(this).next(".btn_clear").toggle(!!this.value);
});
$(document).on("touchstart click", ".btn_clear", function(e) {
  e.preventDefault();
  $(this).prev("input").val("").trigger("input").focus();
});

// ADD , Remove input
var counter = 1,
  custom = $('#custom');
$(function() {
  $('#add_field').click(function() {
    counter += 1;
    var newRow = $('<div class="row' + counter + '"><span class="wrap_input"><input id="exception_' + counter + '" name="" type="text"><button class="btn_clear">clear</button><button class="remove-text-box">Remove</button></span></div>');
    custom.append(newRow);
    (function(index) {
      newRow.find('.remove-text-box').click(function() {
        custom.find('.row' + index).remove();
      });
    })(counter);
  });
});

// clear input value 

$(document).on("input", "input", function() {
  $(this).next(".btn_clear").toggle(!!this.value);
});
$(document).on("touchstart click", ".btn_clear", function(e) {
  e.preventDefault();
  $(this).prev("input").val("").trigger("input").focus();
});

.btn_clear {
  display: none;
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<button id="add_field" href="#">add input</button>


<div id="custom">
  <span class="wrap_input">
    <input type="text" value="">
    <button class="btn_clear">clear</button>
  </span>
</div>

Try to use the following code

// ADD , Remove input
var counter = 1,
    custom = $('#custom');
$(function() {
    $('#add_field').click(function() {
        counter += 1;
        var newRow = $('<div class="row' + counter + '"><span class="wrap_input"><input id="exception_' + counter + '" name="" type="text"><button class="btn_clear">clear</button><button class="remove-text-box">Remove</button></span></div>');
        custom.append(newRow);
        (function(index) {
            newRow.find('.remove-text-box').click(function() {
                custom.find('.row' + index).remove();
            });
        })(counter);

        // call this method after row creation
        setTimeout(function() {
            clearInputValue();
        }, 0);
    });
});

// clear input value
function clearInputValue() {
    $('.wrap_input').each(function() {
        var $inp = $(this).find("input"),
            $cle = $(this).find(".btn_clear");
        $inp.on("input", function() {
            $cle.toggle(!!this.value);
        });
        $cle.on("touchstart click", function(e) {
            e.preventDefault();
            $inp.val("").trigger("input").focus();
            $inp.change();
        });
    });
}