Q: Trojan virus message in Safari asking me to contact 888-681-16.36 for Apple certified technician.  Is this a scare tactic to get me to get expensive service?

These are phishing scams. Do not click on any of the links nor call any telephone numbers.

Identifying fraudulent "phishing" email

Beware of Browser Pop-Up Tech Support, Phishing Scams

Phishing & Other Suspicious Emails

Report phishing email to abuse@apple.com

Remove Browser Pop-up Problems

     Malwarebytes Anti-Malware 1.0.1.7

     Adblock Plus 1.8.9, GlimmerBlocker, or AdBlock

     Remove adware that displays pop-up ads and graphics on your Mac

     How to remove the FlashMall adware from OS X

Helpful Links Regarding Malware Problems

If you are having an immediate problem with ads popping up see The Safe Mac » Adware Removal Guide, remove adware that displays pop-up ads and graphics on your Mac, and MalwareBytes for Mac. If you require anti-virus protection Thomas Reed recommends using ClamXAV. (Thank you to Thomas Reed for this recommendation.) You might consider adding this Safari extensions: Adblock Plus 1.8.9.

Open Safari, select Preferences from the Safari menu. Click on Extensions icon in the toolbar. Disable all Extensions. If this stops your problem, then re-enable them one by one until the problem returns. Now remove that extension as it is causing the problem.

The following comes from user stevejobsfan0123. I have made minor changes to adapt to this presentation.

Fix Some Browser Pop-ups That Take Over Safari.

Common pop-ups include a message saying the government has seized your computer and you must pay to have it released (often called "Moneypak"), or a phony message saying that your computer has been infected, and you need to call a tech support number (sometimes claiming to be Apple) to get it resolved. First, understand that these pop-ups are not caused by a virus and your computer has not been affected. This "hijack" is limited to your web browser. Also understand that these messages are scams, so do not pay any money, call the listed number, or provide any personal information. This article will outline the solution to dismiss the pop-up.

Quit Safari

Usually, these pop-ups will not go away by either clicking "OK" or "Cancel." Furthermore, several menus in the menu bar may become disabled and show in gray, including the option to quit Safari. You will likely have to force quit Safari. To do this, press Command + option + esc, select Safari, and press Force Quit.

Relaunch Safari

If you relaunch Safari, the page will reopen. To prevent this from happening, hold down the 'Shift' key while opening Safari. This will prevent windows from the last time Safari was running from reopening.

This will not work in all cases. The shift key must be held at the right time, and in some cases, even if done correctly, the window reappears. In these circumstances, after force quitting Safari, turn off Wi-Fi or disconnect Ethernet, depending on how you connect to the Internet. Then relaunch Safari normally. It will try to reload the malicious webpage, but without a connection, it won't be able to. Navigate away from that page by entering a different URL, i.e. www.apple.com, and trying to load it. Now you can reconnect to the Internet, and the page you entered will appear rather than the malicious one.

It's a scam; unless you've explicitly chosen to run an Internet-based scanning tool, which are only available for Windows, all messages in a web browser 'warning' of malware are scams.

Choose Force Quit from the Apple menu, close Safari, and then launch it with the Shift key held down. If the message reappears, disconnect the computer from the Internet for long enough to erase that site from the browser history.

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