When we connect a battery in an electric circuit, does it provide the electrons present at anode, or are they the electrons present in the wire?
When you connect a battery to a wire, the electrons in the wire are moved by the electric field provided by the EMF of the battery. As this is a stationary circuit, as many electrons are flowing out from the cathode into the wire as are flowing back into the anode. Thus at the battery cathode, electrons flow into the wire replacing those that are moved away by the electron current flow in the wire. At the anode, electrons coming from the wire enter the battery.
Electrons are already present within the wire. Some electrons are also present in the battery, but electric circuits do not create or destroy electrons. This is important to the conservation of matter.