Good. Something you installed has brought with it some ads... since you haven't detected anything illicit with anti-virus software (unless one of them brought it! which can happen if you use lesser names, for sure...), it's probably (*probably*) not ad-ware... and which one brought it depends largely on what you installed.
The drastic approach: back up all data, factory reset the Note 3. That wipes it back to essentially Safe Mode condition even in normal bootup mode. Then put one app onto the Note 3 at a time, wait 1/2 day to be sure it isn't bringing the ads, then another app, another 1/2 day, and so forth. (Less than 1/2 day if you use the Note 3 a lot, of course.)
The cautious approach: list everything you added on. Think about what you need. Remove the un-needed or not absolutely needed ones, all of those. See if that removes the ads, in normal bootup mode not Safe Mode. (To get out of Safe Mode: just restart normally.)
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