Q: safari not working keep getting message safari can't verify the identity of the website message

Hey Donna, 

I understand that you are getting a pop up that Safari can't verify the identity of the website you are trying to visit. Let's go over some troubleshooting to get this sorted out. 

The first thing I would look at is to see if you have an Extensions on that may be causing this to happen. Take a look at the article below to go over this as well as clearing out cache and cookies for Safari. 

If Safari doesn‘t load a page or webpage items are missing
https://support.apple.com/en-us/HT204098

Take it easy

Hi Donna, 

To clear the caches, you will need to enable the Develop menu for Safari. Open up Safari Preferences by clicking on the drop down menu Safari > Preferences, navigate to the Advanced tab. At the bottom of this window you will see a check box to enable the Develop menu. Then Click Develop > Empty Caches and you will be good to go.

For the Cookies, you will need to open up the Safari Preferences menu again and go to the Privacy tab. Click on the Remove All Website Data... button to get ride of everything. Another option is to wait about a minute and click on the Details... button that appears to clear out only a select few. 

Take a look at the articles below for more details. 

Safari 9 (El Capitan): Use the Safari Develop menu
https://support.apple.com/kb/PH21491​

Safari 9 (El Capitan): Manage cookies and website data
https://support.apple.com/kb/PH21411​

Have a good day