I know about 2 types of sun's motions that sun's spinning motion and the solar apex. Some one told me that there is 3rd kind of motion of sun as well. Can anyone please tell me this 3rd type of motion of sun.

How about traverse of space/time

This depends on what frame of reference you're talking about.

If you're talking about viewing the sun from the earth, the three types of motion are Rotation (movement of the surface of the sun itself), Traversal (moving across the sky from horizon to horizon each day), and Translational, the apparent north-south movement between seasons.

If you're talking about in the galactic sense, you have Rotation (the rotation of the Sun itself), Revolution (the movement of the Sun within this galaxy, orbiting the center), and a third that doesn't really have a good name, which is the apparent motion relative to other galaxies within the universe.

There is also a slow vertical [relative to the galactic plane] bobbing motion as the sun moves along its orbit within the Orian arm.

Professor Astronomy

Could also be the differential motion between the sun's equator and poles. Because the sun is plasma it doesn't rotate uniformly so the equator rotates faster than the poles. This differential rotation is also a major contributing factor to the change in the sun's magnetic field polarity every 11 years.