1. When you have every intention of meeting "that" guy for a drink...but don't want him to asume it.
"Ok, I may show up accidentally on purpose"
2. Deliberately, but feigning (not by) accident.
The first printed record of this phrase is from The history of the famous preacher Friar Gerund de Campazas, by José Francisco de Isla, 1772:
Tell us what is Modesty of Voice, for you happened accidentally on purpose to drop this word, and I don't rightly know what it signifies.
Accidentally on Purpose was an American television situation comedy series, which premiered on CBS on September 21, 2009 and concluded on April 21, 2010.
as if by accident, but really on purpose
They started the fire accidentally on purpose.
The act of "accidentally" discovering something that was in fact, planned by you ahead of time in order to help you acheive your master plan that you were working for all along.
It was "accidentally on purpose" that DJ found another six pack of beer, just what she needed to seduce the unknowing country boy.
A spur-of-the-moment decision to do something that you should not be doing, which you then deny when someone finds out about it by saying it was completely on accident.
Girl 1: Did you steal my favorite shirt? I found it in your room
Girl 2: Oh! Uhh, I must have, um, packed it in my bag by mistake when I was leaving your house! It was on accident!
Girl 2: Yeah, right, accidentally on-purpose!
Phrs. Seemingly accidental but with veiled malice or harm. Childish in nature, but not necessarily confined to children. Associated with the British.
"Tommy broke the TV kinda, accidentally-on-purpose, you know..."