search and paginate inside of dropdowm-menu

I'm new to web applications in general, and I'm starting with Rails. I'm trying to create a dropdown menu in the html.erb file using the form.collection_select command, but I'd like it to include Paginate and Search Item. The biggest issue is pagination; I spent several days searching in the internet but was unable to find any solution. I could add pagination, but it show outof that(I could send link to image in this site beacuse I'm newby here)
, but it isn't what should be.It should be into dropdown-menu and in top of placed Search and in bottom place Paginate as fix place.How do I make a dropdown menu using paginate that is inside the dropdown-menu? javascript? css?