Yes taking Synjardy can make you sleepy.
If you take Synjardy you can experience sleepiness and drowsiness as well as other side effects such as dizziness, headaches, shakiness, weakness, sweating, hunger, fast heart beat as well as confusion.
If you experience some or any of those side effects it would be a good idea to let your doctor know about it.
Not everyone experiences those side effects when taking Synjardy but some people do experience those Synjardy side effects.
Most people take Synjardy without any issue but if you do experience any side effects your doctor should know about it.
Be aware that if you take Synjardy it could make you drowsy and sleepy so you do not want to take Synjardy if you plant to drive or operate machinery.