I'm not sure about that possible interaction in particular, but I do know that the hormones in many types of birth control can interact with certain psychiatric medications. It would be a good idea to ask the prescribing doctors of each medication and the pharmacist. In my experience, not all doctors are aware of the interactions between psychiatric medications and birth control. The information may not even be part of the pharmacist's official, professional information; mine had to do his own research to find a study about it.
Also, if a psychiatric medication affects the effectiveness of a birth control medication, the reverse may also be true. I don't want to give a lot of specifics as references because interactions are very complicated and should always be discussed with doctors. However, one example is Lithium, which interacts with many birth control pills. The Lithium levels in the blood change based on the birth control dose changes over the course of the menstrual cycle. That causes the Lithium to vary in effectiveness throughout the month, which is like taking varying dosages of Lithium.
If Klonopin does decrease the effectiveness of your birth control, your doctor(s) and/or pharmacist may recommend using a form of back-up birth control either all the time or when you're taking the Klonopin regularly.
I will discuss this with my Gyn. and my Psychiatrist at my next appointments with them. i will also talk to the pharmacist. Thank you for your advice.