What is the safest anti anxiety medicine for glaucoma patient?

Narrow or open angle: All commonly prescribed anti-anxiety meds are potentially contraindicated if you have either type glaucoma. CBT therapy might be your best bet in this case. The good thing is that it works if you do. Any drug (not only psychotropic) that causes dilation is risky so you need to always ask your doctor to take glaucoma into consideration when they prescribe. Ask them about this for you specifically.

None are safest: The standard treatment of an anxiety d/o is the triad of temporary Benzodiazepine use, intermediate antidepressant use and talk therapy (like CBT). SSRIs are not contraindicated in glaucoma but there is an elevated risk, so they're best avoided. As for Benzo use, they're not a good idea long term or without the other two parts of the treatment. That leaves us with CBT and lifestyle adjustments.