Já tive essa mesma dúvida, gera confusões mesmo!

Se for no sentido do nosso "de nada", é you're welcome - you are welcome, "your" é o pronome possessivo equivalente a seu/sua.

"You're Welcome" The "You're" here is actually two words "You and Are"

"You're Welcome" means "You are Welcome"

"Your" is one word in this sentance would mean that whoever "your"is owns "Welcome"

Like this is your book.

In response to when someone says "thank you" for giving them something or doing something for them.

It is a short way of saying "you are welcome to ask me for things any time" or "you are welcome to ask me for help any time."

you're is short for you are 

really is it. You are welcome or you're welcome

your is the possesive form of you

The correct is You're welcome.  It is like "de nada" in Spanish