I think Phil0124 & macJack are both right. I was wrong about my site that doesn't push adware/malware - I think it's linked to an ad server my site is using. Once the popup starts, it keeps coming no matter what site you visit - in or out of private mode.
(1) do what macjack says above by clearing your history/data after taking Safari out of memory, then
(3) open Safari and try to browse (not easy - may not work at all), then
(5-don't do this) re-visit that special page that pushes the popup,
......you shouldn't see it again.
What ***** for me is that the site that pushes the popup is something I read daily and is a very popular site. Hopefully, the site owner will notice and remove the ad.
I get this page on my phone when I hit "Close" on the popup:
http://www.googla.com-choose-a-gift-from-amazon-apple-samsung.verygoodads.com/ho me/valid?jkhjkhetjkewhkjth=524;5;192991b49c58b704fed8c71b013f5ec3;82e45b843a8016 19210969fb2b973401;0;659910_0326;http://www.googla.com-choose-a-gift-from-amazon -apple-samsung.verygoodads.com
Hope this helps...