accidently-on-purpose
When you do something 'accidently' but it actually has intention
i.e. Joanna met this guy in the store so all of us are going to bump into him accidently-on-purpose
by accident on purpose
Purposefully inserting the penis into the female's ass during intercourse. When the unwilling female angrily comments the male responds with "it was an accident."
I rammed my penis "by accident on purpose" into my girlfriends ass.
By accident on purpose
When you did not plan on doing something but it happened anyways
So last weekend I spent all my money by accident on purpose because my best friend took me shopping