Two years ago I did a little research on.....

Hi Raisa... you would say..."I did some research (on something)/into something"

im not a native but I think is OK, a research on/into sth

Two years ago, I briefly researched (and here you must say what it was you researched). Example 1: Two years ago, I briefly researched Mitochondrial DNA and its usage in forensic science. Example 2: A few years ago, I studied Mitochondrial DNA and its usage in forensic science.

You can't do "a small research". You could say "I did research on a small something" or "I did some research on something". (Or "a bit of")