Hi  fansari6,
I have created a sample which full fill your requirement.
You need to modify the code according to your requirement.
HTML
<table>
    <tr>
        <td>
            Enter search term:
            <asp:TextBox ID="txtSearch" runat="server" />
        </td>
    </tr>
    <tr>
        <td>
            <asp:TextBox ID="TxtDiagnosis1" runat="server" CssClass="txtmedicine"></asp:TextBox>
        </td>
    </tr>
    <tr>
        <td>
            <asp:TextBox ID="code1" runat="server" CssClass="txtdosage"></asp:TextBox>
        </td>
    </tr>
</table>
<div>
    <link rel="stylesheet" href="https://code.jquery.com/ui/1.10.4/themes/ui-lightness/jquery-ui.css" />
    <script type="text/javascript" src="https://code.jquery.com/jquery-1.10.2.js"></script>
    <script type="" src="https://code.jquery.com/ui/1.10.4/jquery-ui.js"></script>
    <script type="text/javascript">
        $(document).ready(function () {
            map = {};
            $("[id*=txtSearch]").autocomplete({
                source: function (request, response) {
                    $.ajax({
                        url: '<%=ResolveUrl("~/Search_VB.ashx" ) %>',
                        dataType: "json",
                        data: 'prefixText: "' + request.term + '"',
                        success: function (data) {
                            items = [];
                            $.each(data, function (i, item) {
                                var code = item.Code;
                                var shortDesc = item.ShortDesc;
                                map[shortDesc] = { Code: code, ShortDesc: shortDesc };
                                items.push(shortDesc);
                            });
                            response(items);
                        }
                    });
                },
                select: function (event, ui) {
                    var selectedvalue = ui.item.value;
                    var shortDesc = map[selectedvalue].ShortDesc;
                    var code = map[selectedvalue].Code;
                    $("#TxtDiagnosis1").val(shortDesc);
                    $("#code1").val(code);
                    return false;
                },
                focus: function (event, ui) {
                    var selectedvalue = ui.item.value;
                    var shortDesc = map[selectedvalue].ShortDesc;
                    $("#TxtDiagnosis1").val(shortDesc);
                    return false;
                }
            });
        }); 
    </script>
</div>
Search_VB.ashx
<%@ WebHandler Language="VB" Class="Search_VB" %>
Imports System.Web
Imports System.Data.SqlClient
Imports System.Configuration
Imports System.Text
Imports System.Collections.Generic
Imports System.Web.Script.Serialization
Public Class Search_VB : Implements IHttpHandler
    
    Public Sub ProcessRequest(ByVal context As HttpContext) Implements IHttpHandler.ProcessRequest
       
        Dim prefixText As String = context.Request.QueryString(0).Split(":"c)(1).Replace("""", "").Trim()
        Using conn As New SqlConnection()
            conn.ConnectionString = ConfigurationManager.ConnectionStrings("constr").ConnectionString
            Using cmd As New SqlCommand()
                cmd.CommandText = "select ContactName,CustomerId from Customers where ContactName like @SearchText + '%'"
                cmd.Parameters.AddWithValue("@SearchText", prefixText)
                cmd.Connection = conn
                Dim customers As New List(Of Customer)()
                conn.Open()
                Using sdr As SqlDataReader = cmd.ExecuteReader()
                    While sdr.Read()
                        customers.Add(New Customer() With {.Code = sdr("CustomerId").ToString(), .ShortDesc = sdr("ContactName").ToString()})
                    End While
                End Using
                conn.Close()
                context.Response.Write(New JavaScriptSerializer().Serialize(customers))
            End Using
        End Using
    End Sub
 
    Public ReadOnly Property IsReusable() As Boolean Implements IHttpHandler.IsReusable
        Get
            Return False
        End Get
    End Property
    Public Class Customer
        
        Public Property Code() As String
            Get
                Return m_Code
            End Get
            Set(value As String)
                m_Code = value
            End Set
        End Property
        Private m_Code As String
        
        Public Property ShortDesc() As String
            Get
                Return m_ShortDesc
            End Get
            Set(value As String)
                m_ShortDesc = value
            End Set
        End Property
        Private m_ShortDesc As String
        
    End Class
End Class
Search_CS.ashx
<%@ WebHandler Language="C#" Class="Search_CS" %>
using System;
using System.Web;
using System.Data.SqlClient;
using System.Configuration;
using System.Collections.Generic;
using System.Web.Script.Serialization;
public class Search_CS : IHttpHandler
{
    public void ProcessRequest(HttpContext context)
    {
        string prefixText = context.Request.QueryString[0].Split(':')[1].Replace("\"", "").Trim();
        using (SqlConnection conn = new SqlConnection())
        {
            conn.ConnectionString = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
            using (SqlCommand cmd = new SqlCommand())
            {
                cmd.CommandText = "select ContactName,CustomerId from Customers where ContactName like @SearchText + '%'";
                cmd.Parameters.AddWithValue("@SearchText", prefixText);
                cmd.Connection = conn;
                List<Customer> customers = new List<Customer>();
                conn.Open();
                using (SqlDataReader sdr = cmd.ExecuteReader())
                {
                    while (sdr.Read())
                    {
                        customers.Add(new Customer() { Code = sdr["CustomerId"].ToString(), ShortDesc = sdr["ContactName"].ToString() });
                    }
                }
                conn.Close();
                JavaScriptSerializer serializer = new JavaScriptSerializer();
                serializer.MaxJsonLength = Int32.MaxValue;
                context.Response.Write(serializer.Serialize(customers));
            }
        }
    }
    public class Customer
    {
        public string Code { get; set; }
        public string ShortDesc { get; set; }
    }
    public bool IsReusable
    {
        get { return false; }
    }
}
ScreenShot
