Replace Title Menu with My Own HTML/CSS DropDown Title Menu

I don't recommend to replace the SharePoint menus and I'm not sure what you try to replace here, but maybe the following is a starting point for you.

Via CSS you could hide the title bar content (#suiteBarLeft {display:none}). But to add new HTML Content you have to alter the basic aspx sites of SharePoint - this is usaually a bad idea. So the best way would be to use jQuery/Javascript (then you are compatible with SharePoint 2016/online as well).

I'm not sure how technically firm you are... Here is a quick and dirty option (for a single page):

• Go to a Page with webparts (e.g. a list or a web part page)
• Click on the little gear wheel on the right top and choose "edit page"
• Click on "add a web part"
• Choose a script editor from media and content
• Click on Edit Snipptet
• Insert Your Javascript

Try something like this:

<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>

<script>
    $('#suiteBarLeft').html('Your Menu stuff');
</script>

If this is what you wanted:

• Better put the code into a seperate file placed in the site assets (you have to use a content editor webpart instead of a script editor)
• if you want to deploy it on every site, don't use a webpart, but load your Javascript via a custom action.

With JS it would be something like this:

Site siteOBJ = ctx.Site;
UserCustomAction customActionOBJ = siteOBJ.UserCustomActions.Add();
customActionOBJ.Location = "ScriptLink";
customActionOBJ.ScriptSrc = "[PATH_TO_YOUR_SITE]/SiteAssets/js/myMenu.js";
customActionOBJ.Sequence = 1000;
customActionOBJ.Update();
ctx.ExecuteQuery();