This is a word that my sister & I & our friends all used in the 70' & 80's as kids growing up.
It meant that you did something on purpose, (possibly something you already suspected wasn't a great idea)
but a larger unexpected outcome that resulted was an accident.
I was skipping stones in the lake & I accidentally on purpose hit Christina in the head with a rock. (true story...why was I skipping stones in the direction of anyone's head!!)
In 7th grade I accidentally on purpose flooded the home ec classroom with suds because I decided to throw a bar of soap into the dishwasher to see what happened after the teacher specifically pointed out that we should only use dishwasher detergent. (true)
I accidentally on purpose got a huge burn blister on my thumb when I pressed it on the outside of the waffle iron at my godmother's house to see if the outside was also hot like the inside. (also true)