How can I use a custom created mapbox style along with leaflet

with current Mapbox version:

1. after you created your own style, click "Share..." at right top menu
2. You get popup, select Develop "Third Party" and in dropdown "CARTO"
3. copy "Integration URL". This is the link you need for Leaflet.js to set value for the 'tileLayer' object

I successfully added a mapbox style to leaflet

On this URL https://www.mapbox.com/studio/styles/ select your style. Ill use a default style for this example (i think this one is available to all) https://www.mapbox.com/studio/styles/mapbox/streets-v10/share/

Then on this page select the leaflet tab

Copy the Url and use like so in your js file

var map = L.map('map');

L.tileLayer('https://api.mapbox.com/styles/v1/mapbox/streets-v10/tiles/256/{z}/{x}/{y}?access_token=pk.eyJ1IjoibWFza290YSIsImEiOiJjaXp0bmI3M3EwMDBvMndzMHJudnlsMDllIn0.jV7rTNmfiqjx57usCu54rQ', {
maxZoom: 18,
attribution: 'Map data &copy; <a href="http://openstreetmap.org">OpenStreetMap</a> contributors, ' +
'<a href="http://creativecommons.org/licenses/by-sa/2.0/">CC-BY-SA</a>, ' +
'Imagery © <a href="http://mapbox.com">Mapbox</a>',
}).addTo(map);

It's really simple.

The URL to use your map as a tile map:

https://api.mapbox.com/styles/v1/YOUR_USERNAME/YOUR_STYLE_ID/tiles/256/{z}/{x}/{y}?access_token=YOUR_ACCESS_TOKEN

If you want to copy/import a style to your studio account:

https://www.mapbox.com/studio/styles/add-style/THE_USERNAME/THE_STYLE_ID/