What Medicine Do Psychiatrists Usually Prescribe For Anxiety Without Siezures Or Panic Attacks?

depends on the exact nature.
Most commonly in the west in benzodiazapines such as alprazolam or clonazepam. (over here, we also still use barbiturates and meprobamate) Sometimes, they will also an anti depressant such as an SSRI or tricyclic to get to the route of the anxiety. Or an antiphysotic such as olazapine or prochlorperazine if your anxiety has bizarre qualities such as being anxious that major league baseball is trying to assassinate you.
One of the newer anti anxiety drugs is Buspirone.
I’ve also seen Beta blockers like Clonidine being used to help control anxiety as well, they work by blocking the effects of adrenaline.
All in all, its a complex disorder to manage and has many treatment options best chosen by one on one in person consult with a professional.