What is that frog toy that Misaka loves?
It is very possible that you have seen it several times in the anime ( even in the game), it is a gekota


  Gekota (ゲコ太 Gekota?) is a popular mascot found in merchandise marketed to children in the Toaru Majutsu no Index universe. A Gekota fan is called a Gekoer. Misaka Mikoto is a huge fan of the franchise it belongs to, and much to her consternation gets her labeled as someone who is childish. 
  


And without a doubt there is also real life merchandise, and allot of look alike products, with a few samples bellow.