Accidentally on purpose
The idiom is a humorous one, and has existed since the 1700s, where in ‘The history of the famous preacher Friar Gerund de Campazas’, by José Francisco de Isla (1772), it is written: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.
Today the idiom is a popular one. The American poet Robert Frost used it for the title of a poem, where he wonders if the universe was created accidentally or on purpose.
I didn’t want to wear the shirt my mother chose for me, so I accidentally on purpose dropped some tea on it.
There’s no way that Jessica and Jonathan would have met without my meddling. I arranged it all and made it seem as if it had happened accidentally on purpose.
He said he tripped and crashed into his team mate, but I suspect it was done accidentally on purpose. They’ve never liked each other.