How we call recursive function in node js

As @jonrsharpe suggested, move the function outside of the export:

let nestedChildren = function(arr, parentId) {
    var out = [];
    for (var i in arr) {
        if (arr[i].parent_id == parentId) {
            var children = nestedChildren(arr, arr[i].id);

            if (children.length) {
                arr[i].subCate = children;
            }
            out.push(arr[i]);
        }
    }
    return out;
};

module.exports = {
    nestedChildren,
    cleanCode: function(){
        return 'clean code helper';
    }
};

Properties of an JavaScript Object cannot reference themselves or any other property of the same object. Thus, a recursive function within an object is not possible.

To work around this problem, you can move the function to the upper scope (outside of the object) where it's accessible from within the object.

So what I did was defining the function outside of the object as standalone function and then I referenced it in your export.

module.exports = {
    nestedChildren,
    ...
};

is just a shorthand for

module.exports = {
    nestedChildren: nestedChildren,
    ...
};