You’re the best is correct. “Your the best” is incorrect and you should not use this phrase in English.
You’re the best is a contraction of “you are the best”
“Your the best” is a very common mistake in English because “your” and “you’re” sound very similar and have similar meanings.
“Your” is the possessive pronoun of you. This means that we use “your” when something belongs to “you”.
That is your car(you own the car).
“You’re” is the same as “you are”. It is a contraction which means we put two words together often when we are speaking.
The phrase “to be the best” needs the verb “to be” to function and for that reason, the correct way is “you’re the best”.
You’re the best example sentences
Thank you so much for driving me to the airport.
You’re the best.
You’re the best guitar player I have ever seen!