  We first apply the transformation of mixing azimuthal and internal coordinate
to the 11D M-theory with a stack N M2-branes to find the spacetime of a stack
of N D2-branes with Melvin one-form in 10D IIA string theory, after the
Kaluza-Klein reduction. Next, we apply the Melvin twist to the spacetime and
perform the T duality to obtain the background of a stack of N D3-branes. In
the near-horizon limit the background becomes the Melvin field deformed $AdS_5
\times S^5$ with NS-NS B field. In the AdS/CFT correspondence it describes a
non-commutative gauge theory with non-constant non-commutativity in the Melvin
field deformed spacetime. We study the Wilson loop therein by investigating the
classical Nambu-Goto action of the corresponding string configuration and find
that, contrast to that in the undeformed spacetime, the string could be
localized near the boundary. Our result shows that while the geometry could
only modify the Coulomb type potential in IR there presents a minimum distance
between the quarks. We argue that the mechanism behind producing a minimum
distance is coming from geometry of the Melvin field deformed background and is
not coming from the space non-commutativity.
