I have got a patch of blue skin in my back from few days what can it be?

Blue stain. It could be a bruise , a stain from clothing, drug reaction, see your doctor if it is not either of the first two.
Doctor can evaluate. Blue is an unusual color for a new spot on the skin, so if it is not a bruise or a ink/chemical stain, a primary care doctor or a dermatologist can evaluate to see what it might be.