Hi  JOYSON,
I have created a sample which full fill your requirement you need to modify the code according to your need.
Refer below sample code.
SQL
CREATE TABLE [dbo].[UserRegistrationDetails](
	[UserID] [int] IDENTITY(1,1) NOT NULL,
	[FirstName] [nvarchar](max) NULL,
	[LastName] [nvarchar](max) NULL,
	[Gender] [nvarchar](max) NULL
) ON [PRIMARY]
HTML
<div>
    <button type="button" class="btn btn-info btn-lg" data-toggle="modal" data-target="#myModal">
        Open Modal</button>
    <div id="myModal" class="modal fade" role="dialog">
        <div class="modal-dialog" style="width: 400px;">
            <div class="modal-content">
                <div class="modal-header">
                    <button type="button" class="close" data-dismiss="modal">
                        ×</button>
                    <h4 class="modal-title">
                        Registration</h4>
                </div>
                <div class="modal-body">
                    <table>
                        <tr>
                            <td>
                                <span class="text-danger">First Name: </span>
                            </td>
                            <td>
                                <asp:TextBox ID="txtFirstName" CssClass="form-control" Width="250px" runat="server" />
                            </td>
                        </tr>
                        <tr>
                            <td>
                                <span class="text-danger">Last Name: </span>
                            </td>
                            <td>
                                <asp:TextBox ID="txtLastName" CssClass="form-control" Width="250px" runat="server" />
                            </td>
                        </tr>
                        <tr>
                            <td>
                                <span class="text-danger">Gender: </span>
                            </td>
                            <td>
                                <asp:RadioButtonList ID="rblGender" CssClass="radio-inline" runat="server">
                                    <asp:ListItem Text="Male" Value="M" />
                                    <asp:ListItem Text="Female" Value="F" />
                                </asp:RadioButtonList>
                            </td>
                        </tr>
                    </table>
                </div>
                <div class="modal-footer" style="text-align: center">
                    <button id="btnSave" type="button" class="btn btn-primary" data-dismiss="modal">
                        Save</button>
                    <button type="button" class="btn btn-default" data-dismiss="modal">
                        Close</button>
                </div>
            </div>
        </div>
    </div>
</div>
<div>
    <style type="text/css">
        body
        {
            font-family: Arial;
            font-size: 10pt;
        }
        table
        {
            border: 0px solid #ccc;
        }
        table th
        {
            background-color: #F7F7F7;
            color: #333;
            font-weight: bold;
        }
        table th, table td
        {
            padding: 5px;
        }
    </style>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
    <script type="text/javascript" src="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
    <link rel="stylesheet" href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" />
    <script type="text/javascript">
        $(function () {
            $('[id*=btnSave]').click(function () {
                var UserDetail = {};
                debugger;
                UserDetail.FirstName = $('[id*=txtFirstName]').val();
                UserDetail.LastName = $('[id*=txtLastName]').val();
                UserDetail.Gender = $('[id*=rblGender] input:checked').val();
                $.ajax({
                    type: "POST",
                    url: "Default.aspx/UserDetails",
                    data: '{UserDetail :' + JSON.stringify(UserDetail) + '}',
                    contentType: "application/json; charset=utf-8",
                    dataType: "json",
                    success: function (response) {
                        alert(response.d);
                    },
                    failure: function (response) {
                        alert(response.responseText);
                    },
                    error: function (response) {
                        alert(response.responseText);
                    }
                });
            });
        });
    </script>
</div>
C#
[WebMethod]
public static string UserDetails(UserDetail UserDetail)
{
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand("INSERT INTO UserRegistrationDetails VALUES(@FirstName,@LastName,@Gender)"))
        {
            cmd.Parameters.AddWithValue("@FirstName", UserDetail.FirstName);
            cmd.Parameters.AddWithValue("@LastName", UserDetail.LastName);
            cmd.Parameters.AddWithValue("@Gender", UserDetail.Gender);
            cmd.Connection = con;
            con.Open();
            cmd.ExecuteNonQuery();
            con.Close();
        }
    }
    return "Data Saved Successfully";
}
public class UserDetail
{
    public string FirstName { get; set; }
    public string LastName { get; set; }
    public string Gender { get; set; }
}
VB.Net
<WebMethod()> _
Public Shared Function UserDetails(UserDetail As UserDetail) As String
    Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Using con As New SqlConnection(constr)
        Using cmd As New SqlCommand("INSERT INTO UserRegistrationDetails VALUES(@FirstName,@LastName,@Gender)")
            cmd.Parameters.AddWithValue("@FirstName", UserDetail.FirstName)
            cmd.Parameters.AddWithValue("@LastName", UserDetail.LastName)
            cmd.Parameters.AddWithValue("@Gender", UserDetail.Gender)
            cmd.Connection = con
            con.Open()
            cmd.ExecuteNonQuery()
            con.Close()
        End Using
    End Using
    Return "Data Saved Successfully"
End Function
Public Class UserDetail
    Public Property FirstName() As String
        Get
            Return m_FirstName
        End Get
        Set(value As String)
            m_FirstName = value
        End Set
    End Property
    Private m_FirstName As String
    Public Property LastName() As String
        Get
            Return m_LastName
        End Get
        Set(value As String)
            m_LastName = value
        End Set
    End Property
    Private m_LastName As String
    Public Property Gender() As String
        Get
            Return m_Gender
        End Get
        Set(value As String)
            m_Gender = value
        End Set
    End Property
    Private m_Gender As String
End Class
ScreenShot
