Singleton httpclient vs creating new httpclient request

I am trying to create layer for webservice using HttpClient in my Xamarin.Forms mobile app.

1. without singlton pattern
2. with singleton pattern

in first approach i am creating new http client object in each new request made by mobile applicaiton.

here is my code

  public HttpClient GetConnection()
        {

            HttpClient httpClient = new HttpClient();
            httpClient.BaseAddress = new Uri(baseAddress); 
            httpClient.Timeout = System.TimeSpan.FromMilliseconds(timeout);


            return httpClient;

        }

post request code

 public async Task<TResult> PostAsync<TRequest, TResult>(String url, TRequest requestData)
        {
            HttpClient client = GetConnection();
            String responseData = null;
            if (client != null)
            {

                String serializedObject = await Task.Run(() => JsonConvert.SerializeObject(requestData, _jsonSerializerSettings));
                var jsonContent = new StringContent(serializedObject, System.Text.Encoding.UTF8, "application/json");
                HttpResponseMessage response = await client.PostAsync(new Uri(url, UriKind.Relative), jsonContent);
                responseData = await HandleResponse(response);


                return await Task.Run(() => JsonConvert.DeserializeObject<TResult>(responseData, _jsonSerializerSettings));


            }
            else
            {

                throw new NullReferenceException("NullReferenceException @ PostAsync  httpclient is null WebRequest.cs");

            }

        }

client will use following code to execute request

new LoginService(new WebRequest()).UserLogin(userRequest);

inside class that implements IWebRequest _webRequest.PostAsync(Constants.USER_LOGIN, userRequest);

in second approach i am reusing the same http client object in each new request here , my singleton class is thread safe too.

private static readonly Lazy<HttpService> lazy =
        new Lazy<HttpService>(() => new HttpService());

        public static HttpService Instance { get { return lazy.Value; } }



        private HttpClient getConnection()
        {

            client = new HttpClient();
            client.Timeout = System.TimeSpan.FromMilliseconds(timeout);

            //client.MaxResponseContentBufferSize = 500000;
            client.BaseAddress = new Uri(baseAddress);
            return client;
        }

post request code

public Task<HttpResponseMessage> sendData(String url,String jsonData)
        {

            var jsonContent = new StringContent(jsonData, System.Text.Encoding.UTF8, "application/json");

            return getConnection().PostAsync(new Uri(url, UriKind.Relative), jsonContent);
        }

client will use following code to execute

HttpService.Instance.sendData(...)

i have gone through many libraries like RestSharp over web just to explore the best and i found that most of them are creating new objects per request. so i am confused which pattern fits best.