The Indian tree which is said to release Oxygen 24 is the Peepal Tree.
Having said that, it is not entirely accurate to suggest that it releases Oxygen around the clock.
The case with most plants is that they generally tend to take in Co2 and release Oxygen during the day (the opposite to humans). This is known as photosynthesis. At night, however, they follow the human pattern of intaking oxygen and exhaling Co2 - known as respiration.
The difference with the Peepal tree is that it has the capability of also intaking Co2 at night, due to a specific type of photosynthesis that is unique to only this type of plant. That being said, the amount of oxygen it releases during the night is not a large quantity at all.
With that said, we know that the Peepal tree is capable of giving off oxygen both day and night, but it is not necessarily always the case.
I hope this helps!