The code you provided is prone to SQL injection. Always use Parameters.Add() to add parameters/dynamic values to your SqlCommand object. However, I think you helper(
) does not support that. You can change your helper if you want your code to be more secure.
Coming back to the problem you are facing:
You are not using wild card characters(%) in your search query. Replace the SQLCommand query with the one given below:
DataTable dtSearch = VMR.MySqlHelper.GetDataTable("select * from table_name where S_ID = '" + txtSearch.Text + "' OR Fellow_name like '%" + txtSearch1.Text + "%'");