Facing this error : "The INSERT statement conflicted with the FOREIGN KEY constraint "FK_tb_stadmdet...

The issue is in Admission.aspx.cs page, you have the below code.
protected void GridView1_SelectedIndexChanged1(object sender, EventArgs e)
    {
        string value1 = GridView1.SelectedRow.Cells[4].Text;
        string value2 = GridView1.SelectedRow.Cells[5].Text;
        //Label1.Text = value1;
        //Label1.Text = Session["tm"].ToString();
        Session["prgfee"] = GridView1.SelectedRow.Cells[6].Text;
        //Label1.Text = Session["prgfee"].ToString();
        if (Convert.ToInt32(value1) <= Convert.ToInt32(Session["tm"]))
        {
            obj.Save_Rec(objprp);
            Response.Redirect("~/confirm.aspx");
        }


You are not setting objprp to some value. Before that You are setting

 nsadm.clsstadmdetprp objprp = new nsadm.clsstadmdetprp();
so all the columns in the objprp will be set to 0 if its int. In your case usercode is int, so it sets null.this save method tries to save with userid as 0, but there are no records for userid in tb_usr table for value 0. So throwing error "foreign key conflict"
Get the user details in session and set to objprp in admission.aspx page

ya sure, i have shared the code, you can check it

basically what i am doing here is,

student will register first(register.aspx),  (table tb_usr gets the value when user registers), than after his successful registration, he will be redirected to the page(admission.aspx) where he can take admission in a particular programme,and when he opt to take admission, error occurs that i asked for.

I meant the user code which you are trying to save in admission table. Does that particular user has a record in user table?

this is because the column usercode which you are passing and trying to save is not present in table User.

Check whether the usercode exists in tb_Usr