Use event SelectedIndexChange of Dropdownnlist

Use Autopostback="true"

<asp:dropdownlist id="DropDownList1" runat="server" onselectedindexchanged="DropDownList1_SelectedIndexChanged" AutoPostBack="true" >

And you need to turn on the viewstate. EnableViewState="true"

Also make sure the event name is correct. It should be OnSelectedIndexChanged not SelectedIndexChanged. Also check the event name matching on both codebehind & ASPX

protected void DropDownList1_SelectedIndexChanged(object sender, EventArgs e)
        {
            
        }

Also another issue & solution(Not sure your issue is same as this one)
Detect DropDownList SelectedIndexChanged on Page Load[^]

Gotcha I found that link
ASP.NET: Error: DropDownList OnSelectedIndexChanged Event Not Firing[^]

You're going right. But the only thing you've missed off is setting

AutoPostBack=True

of the DropdownList.

Don't forget to set AutoPostback true of DropdownList. Always keep that in mind.