do cyclones and anti cyclones occur in fronts or air masses?

Answer 1

Fronts are just dividing lines between two air masses. The cyclone or anticyclone itself will form in an air mass. In the northern hemisphere, a cyclone (counter clockwise rotation) forms in a low pressure system and an anticyclone (clockwise rotation) forms in a high pressure system.

Answer 2

Permanent or quasi-permanent anticyclones are usually the regions where air masses form.Of these, the most important are the sub-tropical belts of high pressure,the polar anticyclone and in winter time,the large continental highs.So,anticyclones produce air masses.
But , the extra-tropical depressions and cyclones have their origin in the polar front.In polar front, two different types of air masses lie side by side without displacing each other.
So,polar fronts produce,the extra-tropical depressions and cyclones.