تكتب هكذا
Sharjah Court of First Instance, Misdemeanors Circuit
You may check the following link to know the difference between a court and circuit:
http://www.pp.gov.ae/mojapps/sessions/searchSessions.do?setL...

According the MOJ website there already exist two First Instance Courts (http://ejustice.gov.ae/portal/page/portal/eJustice MOJ Porta... :

Sharjah Sharia First Instance Court

Sharjah
Al Khan, Near Sharjah power station, beside port Khalid
Tel: +971 6 5024100

Sharjah Federal First Instance Court

Sharjah
Al Khan, Near Sharjah power station, beside port Khalid
Tel: +971 6 5024100

For the sake of uniformity:

If the source text suggests that the misdemeanors are of federal nature than I would translate it as: Sharjah Federal First Instance Court, Misdemeanor Circuit; of or relating to Shariah law: Sharjah Shariah First Instance Court, Misdemeanor Circuit.

However, I wouldn't translate it as a "misdemeanor court" because both of the courts above, operate with one single judge to hear misdemeanor cases amongst other cases.
It seems that all of the First instance courts hear cases relating to misdemeanors:

http://webcache.googleusercontent.com/search?q=cache:kLK4VgE...

If you visit the Abu Dhabi Judicial Department website (http://www.adjd.gov.ae/portal/site/adjd/courts/?language=en) it says that criminal cases are divided in to different circuits, one of which is the "Misdemeanor Circuit" with one judge:

"Criminal Cases which are divided into Criminal Circuits established with three judges, Misdemeanor Circuits and Offenses (Violation) Circuits established with one judge."
Good luck :)