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.