problem with project

To work with time values only (independant of date) try:

TimeSpan tsStart = new TimeSpan(11, 55, 40);
TimeSpan tsEnd = new TimeSpan(13, 30, 20);
TimeSpan tsCheck = new TimeSpan(12, 0, 0);
if (tsStart <= tsCheck && tsCheck <= tsEnd)
    {
    Console.WriteLine("In period");
    }

But normally, you would work with DateTime objects:

DateTime dtStart = DateTime.Parse("11:55:40");
DateTime dtEnd = DateTime.Parse("13:30:20");
DateTime dtCheck = DateTime.Now;
if (dtStart <= dtCheck && dtCheck <= dtEnd)
    {
    Console.WriteLine("In period");
    }

Please try with below code.

protected void Page_Load(object sender, EventArgs e)
{
string a = "11:55:40";
string b = "13:30:20";
string c = "12:00:00";
DateTime dta = Convert.ToDateTime(a);
DateTime dtb = Convert.ToDateTime(b);
DateTime dtc = Convert.ToDateTime(c);
if (dta < dtc && dtc < dtb)
{
Response.Write("Cond success");
}

}

if(1stTime<12.00 && 2ndTime>12.00)
{
  //Yes
}
else
{
   //No
}

Check this article, it'll save lot of time for other questions related to time.
Time Period Library for .NET[^]