IComparer

IComparer example, with numbers first, and empty strings at the end:

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

namespace IComparer
{
    class Program
    {
        public class myCaseInsensitiveComparer : IComparer
        {
            public int Compare(string x, string y)
            {
                bool isXnumeric = int.TryParse(x, out var xInt);
                bool isYnumeric = int.TryParse(y, out var yInt);

                if (string.IsNullOrWhiteSpace(x) && string.IsNullOrWhiteSpace(y))
                {
                    return 0;
                }

                if (string.IsNullOrWhiteSpace(x))
                {
                    return 1;
                }

                if (string.IsNullOrWhiteSpace(y))
                {
                    return -1;
                }

                if (isXnumeric && isYnumeric)
                {
                    return xInt.CompareTo(yInt);
                }

                return string.Compare(x, y, StringComparison.OrdinalIgnoreCase);
            }
        }

        static void Main(string[] args)
        {
            string[] words = { "1", "a", "A", "", "b", "", "B", "C", "c", "", "", "3" };
            IOrderedEnumerable sortedWords = words.OrderBy(a => a, new myCaseInsensitiveComparer());

            foreach (var sortedWord in sortedWords)
            {
                Console.WriteLine(sortedWord);
            }

            Console.WriteLine("Press any key...");
            Console.ReadKey();
        }
    }
}

Result should be something like:

Source you can download from here.