Player’s Handbook

I have a physical copy of the Player’s Handbook which goes into detail about the roguish archetype Assassin. Is it necessary for me to pay 30 dollars for a book that i already have just to gain use of a single subclass or am i missing something?

No, you don't need to buy the whole Player's Handbook to access the assassin roguish archetype. You can buy single archetypes from the store for $1.99 each: https://www.dndbeyond.com/marketplace/source/players-handbook

Just scroll down to the second Additional Options category

Or you can use the homebrew tools to recreate the subclass for free. As long as you don't publish it.