Ajax Search Suggestion module depends upon the core module named Core, so you need to install it.
Steps to install:
1: Using the composer:
For installing the core module you need to run following commands.
composer require wbcomdesigns/module-core:dev-master
2: Through FTP/SFTP:
You can download this core module from the following links
Now connect your FTP/SFTP and upload the modules related folder and files.
Your directory path will be Magento_Root/app/code/Wbcom/Core
(a) The core module is related to Wbcom packages, and for the proper functioning of any packages related to Wbcom, it is strictly required to install this module.