Front wheel bearings change I have a mountain bike - can the front wheel can have 1/4" bearings?

I know that the standard ones are 3/16" but I think mine came with 1/4"

The reason I am concerned is because I changed my front bearings with 1/4" because I thought that this was the appropriate size, and now I can not tighten the cone adequately because it is either to loose or to tight.
Put the 3/16" bearings back in, even if you have to buy some fresh ones.  

Your quarter-inch bearings are not sitting in the bearing raceway right which is causing the too tight/loose problem.

They will never sit right, and if you do ride on them the bearings will run on the wrong parts of the cup and cone races.  This will lead to early failure of the cup and cone.

Bearings are cheap - perhaps one or two cans-of-coke in your local currency.  Fit new right-sized bearings with grease, and it will work better.