Below is sample code for you idea. Please refine this code according to your requirement.
protected void Page_Load(object sender, EventArgs e)
{
if (!IsPostBack)
{
ViewState["textBoxCount"] = 0;
}
}
protected void Button1_Click(object sender, EventArgs e)
{
int textBoxCount =(int) ViewState["textBoxCount"] ;
textBoxCount++;
for (var i = 0; i < textBoxCount; i++)
{
TextBox txt = new TextBox();
Literal lit = new Literal();
lit.Text = "";
PlaceHolder1.Controls.Add(txt);
PlaceHolder1.Controls.Add(lit);
}
ViewState["textBoxCount"] = textBoxCount;
}