<asp:TemplateField HeaderText="Student_ID">
<ItemTemplate>
<asp:LinkButton ID="lblStudent_ID" runat="server"
Text='<%#Eval("Student_ID")%>' CommandName="StudentID"> </ItemTemplate>
Modify your source code as I shown above.I suggest don't go for button click event instead go for command name.
Private gridviewCandidateDetails_ItemCommand(object sender, GridCommandEventArgs e)
{
if(e.CommandName=="StudentID")
{
LinkButton lblStudent_ID=(LinkButton)e.Item.FindControl("lblStudent_ID");
Label lblChild_Name=(Label)e.Item.FindControl("lblChild_Name");
Label lblClass=(Label)e.Item.FindControl("lblClass");
}
}