Can a Turing Machine know if an input string is a description of itself?

Can any Turing machine? $ M $ with description $$, check if an input string $ w $ Is it a description of itself? That is, you can $ M $ be constructed in such a way that $ M $ I can say yes $ w $ = $$ ?

The closest related problem I could find was: Can I build a Turing machine that accepts only its own coding?

But I want to consider the case where $ M $ you must recognize your own description as an intermediate step, and then accept or reject according to that and some additional criteria. it's possible?