This is an example of how you can get a tile image link by click on Leaflet Tile Layer map

get_tile_url.js

/*
  In this example I showed that users can click on map and
  get link of image tile and containt location of clicked position.
  I used Leaflet.js library and a ArcGIS tile service to prove my work.
  You can easily change "samplePosition" and "initialZoom" to move to
  your favourite location and zoom.
  Just open browser console log and click on the link that is appread
  after clicking on map.
*/


// Constants
var singleTileLink = ''
var esriEndpoint = 'https://server.arcgisonline.com/ArcGIS/rest/services/World_Imagery/MapServer/tile/'
var samplePosition = {lat: 47.59, long:2.38}
var initialZoom = 14

// Layer and Map
var mainMap = L.map('map').setView([samplePosition.lat, samplePosition.long], initialZoom);
var esriLayer = L.tileLayer(`${esriEndpoint}{z}/{y}/{x}`);
mainMap.on('click', function (e) {
	singleTileSpecification = getTileURL(e.latlng.lat, e.latlng.lng, this.getZoom());
    singleTileLink = `${esriEndpoint}${singleTileSpecification}`
    console.log(singleTileLink)
});
esriLayer.addTo(mainMap);

// Function
function getTileURL(lat, lon, zoom) {
	var pi = Math.PI;
	var xtile = parseInt(Math.floor((lon + 180) / 360 * (1 << zoom)));
	var ytile = parseInt(Math.floor((1 - Math.log(Math.tan(lat * pi / 180) + 1 / Math.cos(lat * pi / 180)) / Math.PI) / 2 * (1 << zoom)));
	var tileSpecification = `${zoom}/${ytile}/${xtile}`;
	return `${esriEndpoint}${tileSpecification}`;
};