zero knowledge proof application Suppose I have a secret 'X'. Which can be use as a seed to a deterministic random number generator to generate a number 'Y'. Is there any way to prove to others, that I have the secret 'X' which generated this number 'Y' without revealing the secret 'X' using zero knowledge proof, such as Schnorr's protocol.
So let's assume you have the function $f$, which is publicly known, and you publish the value $y = f(x)$. And then you want to prove that you know $x$. You said $f$ is a deterministic random number generator (and I guess you meant a CSPRNG) - but from the given information I guess it's just important that it is one-way?

Anyway, there are two cases for $f$:


$f$ is defined in algebraic structures like finite groups/ rings/ fields and can be expressed as a polynomial, has structure preserving properties (like being bijective), etc. Then it might be possible to create an elegant proof of knowledge for that specific function, similar to Schnorr's protocol. But there is no catch-all method for all possible functions $f$, and it's possible that you can't find a proper proof of knowledge without revealing $x$ - it all depends on the function.
$f$ is actually non-algebraic, e.g. binary input and binary operations, and it most likely does not preserve structure of any kind, for example the practical hash functions and CSPRNGs. Then the following paper might give you an indication how this could be achieved: Zero-Knowledge Using Garbled Circuits: How To Prove Non-Algebraic Statements Efficiently by Jawurek,Kerschbaum and Orlandi (2013). SHA256 was one of the examples in there - however this is a very different kind of proof of knowledge than Schnorr's identification protocol. And of course, in this case it would also depend entirely on $f$, if this works - and if you are willing to accept its overhead. The example  in the paper took around 5 seconds for a single proof of knowledge of a SHA256 preimage.