Can you give a bit more detail please? Maybe post an image of what you are seeing? I am not sure I understand what is dropping down? It sounds like this may be a history of what you have searched for before? 

So, what search engine are you using? Google? Bing? other?

A bit more info and maybe we can help. 

Thank you for replying , I am using windows 10 chrome and Yahoo as my home page. And yes it is previously used requests that are showing up when I type into some search bars. This does not happen all the time but when it does i have tried to remove the previous requests to no avail. Thanks again !

Thanks for more info. The browsers try and “guess” at what you are typing based on previous searches that are similar. If you keep typing, that list will get smaller as the number of matches goes down. When there are no close matches, you see nothing. 
 

Let’s try this first: You might be able to clear those from happening by turning off search suggestions. See this page and try their suggestion. https://support.microsoft.com/en-gb/topic/turn-search-suggestions-off-or-on-32978815-644c-4a41-9390-968af4700aba

If this is just Chrome doing this, try these steps;

How to Turn Off Search and Site Suggestions in the Google Chrome...

1. Open the Google Chrome App.
2. Tap the Three Vertical Dots in the upper right-hand corner.
3. Tap Settings.
4. Tap Privacy.
5. Ensure Search and site suggestions is unchecked.

Note: This will not prevent the Search Engine from recommending websites you've previously visited. You might have to clear browsing history to stop that, or switch to “new private window” in chrome to stop it from saving your browsing history. I can explain more if needed.

Let me know if either of these work for you  If  or, I can dig a bit deeper