Besty is a very informal word for your best friend — a pet name, the same idea as the spelling you will see more often, bestie. Young people use it in messages and on social media. It is “best” plus a friendly -y ending, the way English makes warm little names (daddy, doggy). In class, in a job letter, or with someone you do not know well, say “best friend” instead. Nobody will be angry if you use it with a close friend; they may only blink at the spelling.