You can create a new search bar by going to https://programmablesearchengine.google.com/cse/create/new. There, you can list different websites and webpages that will show up in search results. Additionally, here you name your search bar, which is helpful if you create multiple custom search bars.

Google has created a website to create a custom search bar, to create your own check the below link. https://programmablesearchengine.google.com/about/. Creating a Custom Search Bar: On this website, anyone can easily program their search bar by just selecting the sites you want to be searched for.