How Can I Filter Customers by assigned to with Current User

Please check the syntax.

frappe.ui.form.on("Your DocType", {
    refresh: function(frm) {
        frm.set_query("customer", function(){
            return {
                "filters": {
                    "assign": frappe.session.user,
                }
            };
        });
    }
});

Please check the filter condition doc.