Decide if a string is a member of a language that represents $P$?

For some enumeration of the complexity class P (such as this as an example: How does an enumerator for machines for languages work?), for each string 𝑝 in the enumeration, does there exist some other string (certificate) 𝑐 that allows you to verify 𝑝 is a member of the enumeration in poly time? I believe that it might be possible in poly time because all we have to do is check if a string fits some certain format (format of the encoding)?

A decision problem $ P$ is poly time verifiable iff there is an algorithm 𝑉 called verifier such that if $ P(w)=$ π‘ŒπΈπ‘† then there is a string $ c$ s.t. $ 𝑉(w,c)=$ π‘ŒπΈπ‘†, if $ P(w)=𝑁𝑂$ then for all strings $ c$ , $ 𝑉(w,c)=$ 𝑁𝑂 and V runs in $ O(w^{k})$ for some constant $ k$ for all inputs $ w$ .