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.
Origin
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.
footnote:
Accidentally on Purpose was an American
television situation
comedy series, which premiered on CBS on September 21, 2009 and concluded on
April 21, 2010.