What effects will a supermassive black hole have on our sun in the near future?
The nearest supermassive black hole is Sagittarius A* at the centre of our galaxy. It is too far away to have any effect on our sun.
In about 4 billion years time the Andromeda galaxy will collide with our Milky Way galaxy. It is possible that the supermassive black hole at the centre of the Andromeda galaxy could get close enough to the sun to have an effect, but this is quite unlikely.