Depends on the job, the medication and the boss.

Some jobs just can't be done if your drowsy or distracted. For any reason. Allowing anyone to work while medicated could put both themselves and others at risk and could set up all sorts of legal ramifications.

Ask your doctor about changing the medication and/or dosage to better control the side effects. Minor changes can have a big effect. Also, if this is a relatively new prescription, your metabolism might adjust and allow you to be more alert. A well timed cup of coffee, usually about fifteen minutes before you get drowsy, might help.

Some bosses will be sympathetic to your case and might give you a break if the job situation allows. Others might cut you some slack for a limited amount of time. Some won't.

With weak unions, right-to-work laws, employees hired as subcontractors, at-will employment and a general lack of worker rights your pretty much on your own if you can't work it out directly with the boss.

Look into changing when you take it depending on the dosage schedule & effects.