The shadow in Illustrator project turns into solid white in After Effects

If you converted the Vector Layer to a shape layer, you have problems. 

If you have applied a Raster effect in Illustrator, then the Raster Effect Resolution should be about 150PPI, and the layer cannot be converted to a shape layer. 

Without seeing the details of the original AI file, It's pretty hard to make an accurate diagnosis. I use Raster effects like Drop Shadow in AI and pull them into AE all the time. As long as you properly setup the layers, you should nave no problems. 

You need to apply the drop shadow effect or the layer style of same name inside AE. A lot of raster based AI stuff simply doesn't translate to AE correctly, which more or less is entirely to blame on Illustrator's deficiencies.

Mylenium 

There's nothing to fix. It's simply not supported and needs to be re-created inside AE. Read the online help on this stuff.

Mylenium