If you're on psych meds, then one would have to contact their doctor about interactions, as well any *SSRI which are anti-depressants to a degree. (Similar classification)
Some drugs, one cannot take with even natural supplements because of interactions, but then again if one is taking either of the above which both are considered SSRIs in some degree, you'd probably have a prescription for your issue of anxiety. Why bother with "Ashwagandha"?
*SSRI: Selective serotonin reuptake inhibitors are a class of drugs that are typically used as antidepressants in the treatment of major depressive disorder and anxiety disorders. The exact mechanism of action of SSRIs is unknown. (I had to look this up to remind myself of what they are, don't be impressed.)
When there are unknowns take great care in even the foods you eat. I recall when depressed one would avoid sugary foods and deserts as well dairy; vitamin C, and more. You've really got to fine tune your life when taking prescriptions for anxiety, and I wouldn't recommend adding anything extraneous until the main issue is under control and with the permission from a doctor while under care.
Bring the label to them and compare notes. Most doctors are quite open to new information and want what is best for their patients. Mine is pretty open but he's Holistic.