CSPRNG generation vs asymmetric encryption performance It might sound like a weird comparison, but which one is faster, If I were to generate a CSPRNG every time or to sign(private encrypt) a data?
It costs a median of about 300 cycles on a modern x86 system to compute the ChaCha pseudorandom function, generating 64 bytes of output from a 32-byte reusable key and a 16-byte input.

It costs a median of about 50000 cycles on a modern x86 system to compute a 64-byte Ed25519 signature.

These numbers are from https://bench.cr.yp.to/.  The fastest signature schemes reported there still cost over 1000 cycles.

But what on earth are you doing where there is any question of whether you should use a PRNG or a public-key signature?  This is like going to a bicycle shop and asking whether you should buy a wheel or a handlebar.  You should identify what your application's goals, threat model, and security needs are first before you try picking the fastest handlebar for your bicycle.

If I screw up my eyes and stand on my head and take your inquiry to mean that you want some properties of a pseudorandom function and some properties of a signature, maybe you want a VRF—but causing onlookers to have to stand on their heads is no way to build a secure system!

P.S.  Signature is a fundamentally different concept from ‘encrypting with the private key’.