"in fits of" is a correct and usable phrase in written English.
You can use it to describe a burst of action or emotion that come in waves. For example: "He laughed in fits of joy when he heard the good news."
He invented rapidly and without indulging in fits of temperament.
They were in fits of laughter and shock.
We just end up in fits of laughter.
Bodies piled on bodies, coordination lost in fits of giggles and yelps.
By now the audience, composed largely of women, was in fits of laughter.
She will unexpectedly break out in fits of screaming and crying.
America's influence is too precious to be squandered in fits of narrow ideological pique.
He wasn't this jerk, screaming at people in fits of temper like Sean Penn or something.
In fits of rage, he would let slip stinging words about her biological mother's crack addiction.
In fits of rage, his daughter, Tania, would bang her fists on a school desk.
Back home, he torments his son in fits of shell-shocked insanity.
