I recently saw text on that picture, over the reddit. It says "If I fits on the Board, I sits on the Board". Since that looks like official and formal signboard, I am curious as to why authors used "fits" and "sits" instead of "fit" and "sit". Are there any suggestions ? Thanks a lot.
It is a very folksy and informal way of talking, as in
If I sees it, I eats it.
usually associated with a form of northern rural speak (Maine, Minnesota) which has been adopted by certain feline dialects.
You also need to consider this is in Minnesota (read: long cold winters leading to cabin fever) at a famous liberal arts college (read: creative types) and they are trying to give the cat a certain personality.
Also, notice the punning in the comments.
This is a "meme" based on videos of cats sitting in boxes that seem to small with the quote "If I fits I sits". This is incorrect language and is intentionally incorrect to sound "cute", perhaps mimicking the way the cat would talk if it could.