Does being having paranoid psychiatric issues cause tremors?

Not directly, but... While there is not a direct relationship between them, paranoia provoke extremely strong anxiety and panic responses, which can cause general tremulousness. Some of the medications used to treat paranoia can also cause tremors or other coordination problems.
Paranoia. Paranoia and severe anxiety and panic attacks can cause tremors due to nervouness and overactivation of the sympathetic system also treatment for these conditions can cause tremors.