If you don’t want Google to give you suggestions on your mobile then you should follow these steps –

• Open Google Chrome
• Click on 3 dots on the top right hand corner
• Tap Settings     
• 
• Then click on privacy (It might show “Privacy and Security” instead of “Privacy” because of Phone brand and chrome version.)
• Now check whether Search and Site Suggestions is checked or not. If it’s checked, then uncheck it.

Now, Google Search Engine will stop recommending sites that you previously visited.

To turn off autocomplete features when you type something in search engine, follow these steps –

• Go to settings and then click on advanced
• Now, tap on Sync and Google Services
• Finally, disable Autocomplete searches and URLs

To delete URL suggestions on laptop, follow these steps –

Start typing a URL, use arrow keys to highlight the one, you want to delete and press Shift and Delete. But, it is tiresome if you have multiple suggestions as you have to delete them individually. Besides, this works temporarily.

So, the better way to remove the URL suggestions permanently is to clear browsing history. Either use the keyboard shortcut Ctrl+Shift+Delete or open Settings, then choose More tools and then click on Clear browsing data. Now, you will get basic and advanced options. In the basic options, tick the box of Browsing history. From the drop down menu, choose how much of your history should be erased – you can erase last 24 hours history to everything. Finally, tap on Clear data.

Also make sure that the site in question is not stored in bookmarks. If it is, then right click it in the bookmarks and delete it.