Possibly AMS is intended for older phones? Regular Adsense for Search should work okay on smart phones. If you choose to have results shown on your site instead of Google's, the layout should probably be changed to fit a narrower screen.
You have to create your own CSE by going to My Ads in your Adsense interface, clicking on "Search" in the left menu, then either clicking "New Custom Search Engine" at the top of the page or clicking on an the name of an existing SE. The options on the first page are limited. For more options suitable for mobile click on the link at the bottom of the page "Access more advanced search features". Click on "Look and Feel" in the left menu to access the layout controls. The Compact style is intended for mobile.