Hi rani,
Using the below article i have created the example.
Database
For this example I have used of Northwind database that you can download using the link given below.
Download Northwind Database
Model
public class Customer
{
    public string CustomerID { get; set; }
    public string ContactName { get; set; }
    public string City { get; set; }
    public string Country { get; set; }
}
Controller
public class HomeController : Controller
{
    private DBCtx Context { get; }
    public HomeController(DBCtx _context)
    {
        this.Context = _context;
    }
    public IActionResult Index()
    {
        return View();
    }
    [HttpPost]
    public JsonResult AutoComplete(string prefix)
    {
        var customers = (from customer in this.Context.Customers
                            where customer.ContactName.StartsWith(prefix == null ? "" : prefix)
                            select new
                            {
                                label = customer.ContactName,
                                val = customer.CustomerID
                            }).ToList();
        return Json(customers);
    }
    [HttpPost]
    public IActionResult Index(string CustomerName, string CustomerId)
    {
        ViewBag.Message = "CustomerName: " + CustomerName + " CustomerId: " + CustomerId;
        return View();
    }
}
View
@addTagHelper*, Microsoft.AspNetCore.Mvc.TagHelpers
@{
    Layout = null;
}
<!DOCTYPE html>
<html>
<head>
    <meta name="viewport" content="width=device-width" />
    <title>Index</title>
    <style type="text/css">
        body {
            font-family: Arial;
            font-size: 10pt;
        }
        .ui-autocomplete {
            overflow: auto;
            max-height: 100px;
        }
    </style>
</head>
<body>
    <script src="https://ajax.aspnetcdn.com/ajax/jQuery/jquery-1.10.0.min.js" type="text/javascript"></script>
    <script src="https://ajax.aspnetcdn.com/ajax/jquery.ui/1.9.2/jquery-ui.min.js" type="text/javascript"></script>
    <link href="https://ajax.aspnetcdn.com/ajax/jquery.ui/1.9.2/themes/blitzer/jquery-ui.css"
          rel="Stylesheet" type="text/css" />
    <script type="text/javascript">
        $(function () {
            $("#txtCustomer").autocomplete({
                source: function (request, response) {
                    $.ajax({
                        url: '/Home/AutoComplete/',
                        data: { "prefix": request.term },
                        type: "POST",
                        success: function (data) {
                            response($.map(data, function (item) {
                                return item;
                            }))
                        },
                        error: function (response) {
                            alert(response.responseText);
                        },
                        failure: function (response) {
                            alert(response.responseText);
                        }
                    });
                },
                select: function (e, i) {
                    $("#hfCustomer").val(i.item.val);
                },
                minLength: 0
            }).focus(function () {
                $(this).autocomplete("search");
            });
        });
    </script>
    <form asp-action="Index" asp-controller="Home" method="post">
        <input type="text" id="txtCustomer" name="CustomerName" />
        <input type="hidden" id="hfCustomer" name="CustomerId" />
        <br /><br />
        <input type="submit" id="btnSubmit" value="Submit" />
        <br /><br />
        @ViewBag.Message
    </form>
</body>
</html>
Screenshot
