My 1month old baby has vibrating leg every now and then whether sitting or sleeping ?

Neurologist: Hello. The symptom you mention is concerning for a neurological disorder. It is very important that your baby is evaluated by a neurologist because diagnosis and treatment at this age is vital for the development of your baby.

Keep an eye on it: Assuming that your baby is fine in all other ways, I would say that involuntary movement is common in an infant. I would become concerned if it worsens with in increasing severity or limbs involved. I would record these movements with you cell phone camera and show your doctor at the next well baby appointment. Call in to your PCP if this worsens.