How do I fill in the White space in the letter!

Oscar,

For a vector artwork letter, the clipping mask solution by Bobby is the straightforward way to go.

For a raster artwork letter, presuming the background transparent rather than white, or even for a vector letter, you can:

1) Create a copy of the letter so you have one instance of the letter both beneath and on top of the PNG background image, you can Ctrl/Cmd+C+F+X+F (hold Ctrl/Cmd and press C then F then X then F) or Ctrl/Cmd+C+F+X+B depending on the current stacking order (see the expanded Layer in the Layers panel); you can lock the letter beneath;

2) Select both the letter on top along with the PNG image, then apply a(n Opacity Mask) with Clip ticked and Invert Mask unticked in the Transparency panel;

3) Group everything, after unlocking the letter beneath if locked in 1).

Always keep a backup of artwork that is to be changed.

If that letter "T" is a vector path (converted from a font) you'll need to release the compound and ungroup the results. Then you'll be able to select the interior part of the "T" and change its color fill or even use it as a clipping mask to contain an image.