As electric field remains the zero inside the conductor so the potential at the surface should be the same as inside, but i came with a situation which is as follows: if a spherical conductor is placed inside (concentrically) a conducting shell which has greater dimensions than that of the first conductor and a some charge is given to the smaller conductor then no work should be done as the potential remains the same however if we weld a metal conductor conducting the two spheres, then we notice that the entire charge Q must be appear on the outer sphere by Gauss's law. I'm not able to understand the two above contradicting statements. Thanks.
It's true that the charged sphere has the same potential everywhere, but it's not true that the potential is the same as any other conductor. In particular, the concentric shell around the sphere will have a potential difference with respect to the sphere, which can be eliminated by connecting the metal conductor connecting the two. The work required for the charges to flow to the outer shell will be equal to the total energy stored in the electric field between the two conductors.
As electric field remains the zero inside the conductor
That "inside" can be read in different ways. If you mean inside the bulk conductor, it is correct. If you mean in the interior portion of a hollow conductor, it may not be correct.
If you have two conducting shells, there will be zero field within the bulk metal of either shell, but there can be a field in the gap between the shells. This will be the case if the interior shell is charged.