Hi trisetia302,
Check this example. Now please take its reference and correct your code.
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 Id { get; set; }
    public string Name { get; set; }
}
Namespaces
using Microsoft.AspNetCore.Mvc;
using System.Collections.Generic;
using System.Data;
using System.Data.SqlClient;
Controller
public class HomeController : Controller
{
    public IActionResult Index()
    {
        return View();
    }
    [HttpPost]
    public IActionResult Index(string CustomerName, string CustomerId)
    {
        ViewBag.Message = "CustomerName: " + CustomerName + "\\nCustomerId: " + CustomerId;
        return View();
    }
    [HttpPost]
    public IActionResult AutoComplete(string Prefix)
    {
        List<Customer> customers = new List<Customer>();
        using (SqlConnection con = new SqlConnection(@"Data Source=.; Initial Catalog = Northwind; UID=sa;PWD=pass@123;"))
        {
            using (SqlCommand cmd = new SqlCommand())
            {
                cmd.CommandType = CommandType.Text;
                cmd.CommandText = "SELECT CustomerID,ContactName FROM Customers WHERE ContactName LIKE @Name + '%'";
                cmd.Connection = con;
                con.Open();
                cmd.Parameters.AddWithValue("@Name", Prefix);
                using (SqlDataReader dr = cmd.ExecuteReader())
                {
                    while (dr.Read())
                    {
                        customers.Add(new Customer
                        {
                            Id = dr["CustomerID"].ToString(),
                            Name = dr["ContactName"].ToString()
                        });
                    }
                }
                con.Close();
            }
        }
        return Json(customers);
    }
}
View
@model jQuery_AutoComplete_Core_MVC.Models.Customer
@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>
    <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
    <script type="text/javascript" src="https://ajax.aspnetcdn.com/ajax/jquery.ui/1.9.2/jquery-ui.min.js"></script>
    <link rel="Stylesheet" type="text/css" href="https://ajax.aspnetcdn.com/ajax/jquery.ui/1.9.2/themes/blitzer/jquery-ui.css" />
    <link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" />
    <script type="text/javascript">
        $(function () {
            $("#txtCustomer").autocomplete({
                source: function (request, response) {
                    $.ajax({
                        url: '/Home/AutoComplete/',
                        data: { "Prefix": request.term },
                        dataType: "json",
                        type: "POST",
                        contentType: "application/json; charset=utf-8",
                        success: function (data) {
                            response($.map(data, function (item) {
                                return {
                                    label: item.Name,
                                    val: item.Id
                                };
                            }))
                        },
                        error: function (response) {
                            alert(response.responseText);
                        }
                    });
                },
                select: function (e, i) {
                    $("#hfCustomerId").val(i.item.val);
                },
                minLength: 1
            });
        });
    </script>
</head>
<body class="container">
    <form asp-action="Index" asp-controller="Home" method="post">
        <label asp-for="Name" class="control-label"></label>
        <input asp-for="Name" type="text" name="CustomerName" id="txtCustomer" class="form-control" />
        <input asp-for="Id" type="hidden" name="CustomerId" id="hfCustomerId" />
        <input type="submit" id="btnSubmit" value="Submit" class="btn btn-primary" />
    </form>
    @if (ViewBag.Message != null)
    {
        <script type="text/javascript">
            window.onload = function () {
                alert("@ViewBag.Message");
            };
        </script>
    }
</body>
</html>
Screenshot
