Partitioning with IEnumerable source

Partitioner.Create(_queue).GetPartitions(4); Partitioner.GetPartions creates 4 partitions but all records are in 1st partition only; 2,3,4 partition are empty.

This is not correct, your queue entries are being partitioned correctly. To verify, change your processing logic slightly to log the partition that is doing the work:

Task t = Task.WhenAll(
    from partition in partitioner.Select((jobs, i) => new { jobs, i })
    select Task.Run(async () =>
    {
        using (partition.jobs)
        {
            while (partition.jobs.MoveNext())
            {
                Console.WriteLine(partition.i);
                await CreateJobs(partition.jobs.Current);
            }
        }
    }));

You will notice that the Console.WriteLine will write values from 0 to 3 - indicating that they are being partitioned correctly.

Also, I want to remove the item from _queue after processing in consumer method and there is only one way _queue.TryTake method to remove item. I don't know how to remove item along with partitioning?

You can achieve that with a slight rewrite. The main changes are switching to BlockingCollection and by adding this NuGet package to give access to GetConsumingPartitioner.

Give this a try:

using System;
using System.Collections.Concurrent;
using System.Linq;
using System.Net.Http;
using System.Threading.Tasks;

namespace Test
{
    public class TestQueue
    {
        BlockingCollection<Job> _queue = new BlockingCollection<Job>();
        private static HttpClient _client = new HttpClient();

        public TestQueue()
        {
            WorkProducerThread();
            WorkConsumerThread();
        }

        public void WorkConsumerThread()
        {
            if (!_queue.IsCompleted)
            {
                //At this point, 4 partitions are created but all records are in 1st partition only; 2,3,4 partition are empty
                var partitioner = _queue.GetConsumingPartitioner().GetPartitions(4);

                Task t = Task.WhenAll(
                 from partition in partitioner
                 select Task.Run(async () =>
                 {
                     using (partition)
                     {
                         while (partition.MoveNext())
                             await CreateJobs(partition.Current);
                     }
                 }));


                t.Wait();

                Console.WriteLine(_queue.Count);
            }
        }

        private async Task CreateJobs(Job job)
        {
            //HttpContent bodyContent = null;
            //await _client.PostAsync("job", bodyContent);
            await Task.Delay(100);
        }



        public void WorkProducerThread()
        {
            if (_queue.Count == 0)
            {
                try
                {
                    for (int i = 0; i < 20; i++)
                    {
                        Job job = new Job { Id = i, JobName = "j" + i.ToString(), JobCreated = DateTime.Now };
                        _queue.TryAdd(job);
                    }

                    _queue.CompleteAdding();
                }
                catch (Exception ex)
                {
                    //_Log.Error("Exception while adding jobs to collection", ex);
                }
            }
        }

    }

    public class Job
    {
        public int Id { get; set; }
        public string JobName { get; set; }
        public DateTime JobCreated { get; set; }
    }
    class Program
    {
        static void Main(string[] args)
        {
            var g = new TestQueue();

            Console.ReadLine();
        }
    }
}