This is a simple guide line to take United Arab Emirates Driving Licence from Sharjah.
A person having Sharjah Visa can only apply for driving licence in sharjah, people with dubai visa can apply in dubai, people with Ajman visa can apply in Ajman, etc. Also a person with any emirate visa can apply in abudhabi.
Also if you are having sharjah visa and your company has a branch in dubai too, then you will be able to apply in dubai even if your visa is stamped in sharjah or any other emirate.