Auth Api

could anyone help explain with a sample code on exactly how a customer can or should register using the Auth api or how it works like

am trying to look for a solution or an Addon that is able to give customers the correct fields required just like in the backend website with feilds like

first name second name email address passoword and phone number basically same form data details from the backend in the restful api dynamically anyone knows how to do this or how it works like or any clear documentation in regards to this