In the way you defined it, no motion relative to the sun, it is not possible to stand still, because the sun itself is not a solid object. Instead different latitudes rotate with different velocities.
You could stand still with regard to the sun's equator by being in a tight orbit around the sun with an orbital period of 24.47 days.
If I understand you correctly, however, you don't want to be in an orbit around the sun. If this is the case, you need to keep firing your engine, so you are not pulled into the sun. As HopDavid correctly pointed out to you, the most plausible concept for this is a Statelite. However, the sun will still be spinning below you, so you are still not fixed in place with regard to most of the sun.
From your question and subsequent replies, I think maybe you may enjoy reading a basic textbook on orbital mechanics. I don't think stackexchange can give you the structured introduction that you need in order to move on in this complicated subject.